I am going to give you the most painful almost brutal advice, but I speak from over 25 years of legal experience
WALK AWAY..

It is not your child, not his child, walk away. Walk away before your entire life becomes that child. It is her child. It is not your child, WALK AWAY.

This is what is going to happen if you don't. The 'Unfit' parent will use the child as a yo yo...pulling your husband to her when ever she wants him. Messing up the child's mind...so that even if you get that child, you are going to hear something about how you took him away from his real mother.

Legally you are a stranger, you have not rights. Walk away. Forget about the child. Or, destroy your lives and your marriage over it.

How old is the child?

this is a very hard situation because i went through the same thing with my ex. he was....and in inherit taking care of two of his ex g/f kids (wasnt his, but he raised them). my ex and his ex g/f would play games with each other while im babysitting. he allowed her to do and say anything disrespectful to me without saying anything in fear that she would not allow him to see the kids.
so i cut her and her kids off, which was a battle with my b/f sister and his mother who adored those kids, and didnt consider what i was going through.
i m bias in this situation because of my past experiences, i would say "hell no" i m not dealing with taking care of a child that's not yours, while she doesnt want us to adopt it, and want my man.
Been there, done it!!!
you have to talk to your husband and tell them your silver lining. how do you feel? what are you willing to put up with? there also have to be a serious talk about this women. "dont allow her in your kitchen". i felt like the other women was always in my kitchen, it's only one women in a kitchen. she was in our lives, in our business, in our arguments. it wasnt worth it, then again he was my b/f not my husband.
so good luck to you.