Credits are totally possible! He needs to go to the office and get a statement though, just so he has the back up is BM comes after him in court. 

My DH always has a credit because they divide a monthly sum owed over 26 pay periods, which comes out more than what he owes. When he changed jobs the Child Support Enforcement Unit was all over it and had the papers to his new job after one pay cycle.  In the meanwhile, he had mailed a check to them, which they promptly returned after the withholding was set up.

Just ask them to send some sort of receipt of payment, I'm sure they will anyway.

He needs to document whatever he can possibly document.  Request a mailed copy of his balance owed (or emailed .. if possible).  He should always get the name of the person he speaks with and mark down the date and time.

When he makes a payment.. he should aslo document how he does that.. if it's over the phone... then he should get the person's information or confirmation number.

When BM calls and asks.. he gives her the relevant information.  I don't know.. here is the person that took the payment information from me on the 3rd.

The beauty of the state taking care of this is so you don't have to listen to BM complain.  He is doing his part to the best of his ability from the sound of it.  Let her call the state agency and take it up  with them.  

He just needs to disregard her complaining.  Simple in theory, harder to practice.  

DH paid through the state but he sent the check to CSE, himself, it was not withheld from his paycheck. That is where so many of the problems lie when changing jobs.

Our county and state have an online portal to log into.   I can see when payments are posted, the balance owed, etc etc.   Google your county website to see if hubby can create an account.   I have printed out statements and used them in court to prove my SIL is in arrears on the grandbabies child support.   I cannot make an online payment but I am the reciever, not the payor so I don't know if that is an option.

I can comiserate with you OP.  My DH's EX was a B on wheels about her CS.  He paid her directly.. so obviously.. she was always ready to ask early and often if he could pay her "early" because I hav a bill etc..

A lot of the time, I was the one actually going to her bank and making the deposits.. so it was kind of a pain on my end.. also.. due to issues that occured over his CS obligation years.. sometimes I was actually paying out of my pocket.. becuase he didn't have it.  I was basically "lending" him the money.. but still.. we didn't really keep tabs on it like that on our end.  There were times BM would tell him "get your wife to pay me" if he was having issues coming up with it..

The bottom line was that I understood that she was owed this money.. I get that she relied on it.. and she had every right to rely on it.  However, I also know on his end.. when he was having problems paying it.. it was for a good reason and it would have been "nice" if she could have had some empathy for his situation as well.  And.. yeah.. she was living with her BF.. and the only real bills she did have were her cell phone bill.. and maybe some charge card stuff.. because usually we or the grandparents were sending the kids food and buying them clothes.. and she paid no rent.. didn't have a car pmt or ins pmt  etc.. so the money truly didn't need to cover the girl's expenses.  BUT... sure.. he had an obligation to pay that money to her.. and he did.  A few days late at times.. but there were other countless situations where he paid her EARLY too.. or gave her extra money for gas etc.. so she would let him have the girls for visitations.

So.. yes.. this IS his obligation... but since you live with him.. I understand how the stress bleeds over to BOTH of you.  I also understand the logic you state about since she has access to "other money".. that why does she have to go all postal on him.  I don't think you are saying that he doesn't need to pay.. but that gosh darn it.. can't your BF spot you with a hundred bucks until the CS agency gets you your money?  You can pay him back when the check DOES come in?  But.. theoretically.. just because I did have funds.. didn't mean that I was obligated to help my DH meet his CS pmts... even though I did do it at times.. it was my choice and it pissed me off when she would tell him that I needed to pay it.. because.. I didn't.