In your home, your DH should be responsible for 100% of his bills, 100% of his daughter's bills and 50% of your shared child's bills. You are responsible for 100% of your bills and 50% of your child's bills.  

Now, if there is some uneven division of financial vs nonfinancial contribution.. then those percentages can be adjusted.  and many couples also will adjust for earning ability if there is a disparity.. where one partner earns markedly more.. they may live in a home or at a higher standard than the lesser earning partner.. in those cases.. the higher earner may pay a higher share because if it were not for them.. their partner would be living more modestly.  It's not fair to ask your partner to pay 100% of their income towards bills.. having zero discretionary.. while it may only take a fraction of your income to match that.. and you have tons of money you can spend as you please.

So.. that's just  a little basics on how it can be reasonable to split bills.

In steplife.. the other parent should be contributing to the wellbeing of a shared child.. so yes.. your DH's EX  "should" contribute to her daughter's upkeep if she lives in your home full time.. she should technically pay support.

But.. let's take a look at reality here.  If your DH's EX is on and off drugs.. not stable employed etc... it is going to be a blood from a stone situation.  To be blunt, she doesn't have the resources to support her daughter.. and probably never will.  So, that ends up being the sucky situation where your DH made a poor choice to breed with someone that was going to dump ALL the responsibility on HIM.  Is it worth him racking up the expense of legal bills if she will likely never have the resources to actually PAY anything?  Unfortunately, it probably isn't worth it.. it would just be money wasted.  Now, if there is a way to get it legally ordered for "free".. he can do that.. but it still is not going to change anything for your household because I highly doubt his EX will ever be able to or will ever pay it.

It's not just that he is choosing to give her a break.. he probably thinks it's a lost cause.. so why bother.

BUT.. that does not mean that within your home that you have to make up the difference.  you need to stand your ground on your share of the household expenses being related to you.. and 50% of your child's... he needs to pick up MORE cost because your SD's costs shouldn't be subsidized by you.  It may not be a huge difference.. but it would be fair for him to pay more.  And.. while you are on maternity leave.. it would also be fair for him to shoulder some of YOUR share because your pregnancy and caring for his baby is why you are not currently working.

And... here is another pill to figure out how to swallow though..   He may not be able to pay more than he already is...so the relative unfairness of the current split... it may be what it may be.  I think you may have to accept his EX may not be capable of paying.. and you may need to accept your SO's resources are also limited in that he may not be able to pay more.. even if that would be the fair thing to do.  Sometimes what's "right" and what is "possible" are not the same.  

I would advise you to not join your finances with him.. I would keep my money separate.. and just give what your joint obligation is to pay bills.. 

In the end, you may decide that he is not the right partner for you.. if you feel the financial situation is too difficult.. you can get child support from him and go raise your child on your own... or with help from him.. but lose the relationship part.  

Just say I am not paying your DD,  Has he gotten a CS order on BM ?  Did he try to get money from BM, as getting her tax refund or is he sitting looking at you.  He now has a bio with you.  He must pay 100% of the bills, you do what you want with your money.  Buy your bio kid nice things. Take trips to the North Pole and Santa land.  They are only young once if that time passes you will never get it back.

I would not let SD control, or effect life with your bio kid.  It may suck for her. 

We had a similar deadbeat situation but it was both of the exs. Mine was a druggie and BM was a lazy, unemployed mooch.  I knew going the legal route would have been a waste of time, money and energy.  So, it was up to DH and me to support and raise all 5 of our kids at our house.

It's a hard pill to swallow and it breeds resentment all around.  We were married and had made our commitment to each other so we did it.  Not easy but the whole situation made us deeper than dirt.  Lol.

Good luck with whatever arrangements you come up with.

Is he your boyfriend or legal husband?  

You have some options, 

Tell him NO OR

Kick his ass out, and file for child support for the baby on the same day. , That is how you send a very clear message you are sick of his bs. 

OR if you DO NOT  want to do that, for what the ever the  reason:  Ask him to produce the legal document that proves you are responsible for his and dirt bag bm's child. OR Pack your bags and move in with your mom/dad AND file for child support the very same day.

You are not morally obligated to support bm's child. That is BM and dads obligation.

*edit to add, Miss, I believe you are being used. Plan accordingly. JMO

Tell your partner to get a second and third job!

Reality is this generation of men is lazy and would rather have their just out of delivery new mom out here working in the trenches with them then stepping up as men and providing for their family 

Don't say anything about his daughter directly because yeah it will cause an argument 

instead spread some classified articles on the kitchen table 

*in the future - don't ever procreate with men who expect 50/50 (half these people can't count and it will never be in your benefit) .... There is no way you should be giving him intimate privileges/ birthing out his child/ and paying half the bills;

men expect half the money from other male roommates or women they don't like .... ijs

***hopefully you didn't marry into this because yeah you kinda take on responsibility for those kids if you're married and your husband is unable to. (This is why I never married my ex Disneyland dad ... realized he was struggling as his exwife selfishly and intentionally ​​​​​​ shirked her responsibilities and knew I didn't have the additional resources to help as an already stretched thin single mom so he would have to help himself by earning a higher income)

Time for daddy to man up and support his wife and baby.  

Keep it simple.

Even in court a SParent's income cannot be considered in setting CS.  So, don't pay CS to your DH for his failed family spawn to let his toxic X off of the hook.

Time to preserve your income and assets and hold daddy accountable for providing.

I would if I were you.

Since he has no CS order in place for hsi first failed family progeny, file not and nail his ass toe the all for a shit pile of CS.  Yours will be the firs in place and will likely be substantial. Maybe then, he will nail his X for CS rather than extorting support out of you for his failed family progeny. 

It is the teen that I feel the most for in all of this. She lost both sides of the parent lottery.  Your new  baby at least won the mom lottery though very likely may have lost the dad lottery.

Leverage your situation for the benefit of you and your LO.  Maybe seeing daddy have his nads held to the grindstone may do your SD some good as well.  It for sure will be a complete benefit to SD to see her deadbeat mommy forced to step up if you can make it painful enough on daddy to man up and do what he should have done long ago.

IMHO of course

"I am not required to, nor will I support a child that is not mine."

Short, sweet, direct, clear, and firm.

In our case, we married the week before SS-32 turned 2yo.  I had no problem being the sole earner in our marriage.  There was a pittance in CS (Initially $110/mo for a year then $133/mo for 9 years before increasing.).  

However, if I had married a partner with an older hid and that kid was a toxic ill behaved spawn, nope. I'm not supporting failed family baggage.

I know that starting a blended family marriage with a toddler married to the CP with full physical and legal custody and living across the country from the NCP is the Unicorn of blended family situations.  Adding that DW and I were always fully aligned on the standards we would require in behavior and performance from our son, in an age appropriate manner, made our family adventure a pleasant one for all three of us. Though it certainly made the toxic PAS, lies, and manipulations of the blended family opposition most decidedly unpleasant for them.

If your SO is not delivering parenting to your standards, make sure he knows that support for his child is entirely on him and BM.   Keep a very tight rein on your assets.