I have more assets than my partner. His pension goes into our joint account. We each keep other assets seperately. I match the amount he has going into the joint account and from there I handle all bills. 

If DH wants to give his skids money he gets it from his savings. If he wants spending money that has to come from his savings too. If he has excess medical bills they come out if his savings.

I like to buy new things for the house, which is in my name so I pay for them myself. If I buy my adult kids things it is out of my savings. Sometimes I have to top up the joint account out of my money and usually I don’t mind.

DH and I have separate bank accounts (not even one joint). All bills get paid from my checking account (which I had set up before DH), so I tell DH what his portion is every month and he transfers money into my account. We split groceries and household stuff (which gets put on a credit card and paid every month) but we don't nickel and dime each other (if he pays cash for a few groceries, he doesn't come home and say, "You owe me 20 bucks".

We both put money into our own savings/checking accounts and we know what we can afford to spend on extras.

DH puts money into it, you put money into it.  You can pay the bills, actually move the money, write checks. with the money from new checking account.  This checking account pays all house hold bills.  Rent, elect, heat, gas, food, car, repairs, insurance, ect.  How you fund it is the big question ? There more of him so he should put more in the account 

I put together a list of our estimated monthly bills and split the total in half and asked that he pay that much each month. I make more and do most of the grocery shopping so I just paid for those myself.

If something cause the monthly bills to be higher we would discuss how we were going to pay it.