How old is the child? It's not easy. But you and your husband have to stick together. And I mean that. My step daughter lied and tried everything she could to get her way and make me the bad guy. And it worked for a bit.....my husband and I had some real issues for a while. Until a neighbor told him that HIS daughter was purposely saying things that were not true.
So, depending on the age of the child, sit them both down (after you talk to your husband first) and explain that this house hold is going to change. There will be respect and if you can't say anything nice, don't say anything at all.
You also don't say how long you have been married to the husband. If it's a new relationship, then give it time. They will work it out. Let your husband make some "good" decisions on some things that the child might want to do and you be the bad guy, even if you agree to whatever it is, so the hubby can show that he's on the kids side too.
You also need to tell the child that there are always people in your life that you don't like, family, co-workers, or people that you deal with at the store, but you do owe them respect and courtesy. It's a part of life, like it or not.
I would also tell the child the benefits not only for you to have this man in your life, but the benefits for the child. Like it or not, when Moms happy most of the time the family is happier too. And I'm sure there are things that benefit the child from this relationship.
Good Luck and hang in there.