An ex wife can be very manipulative and believeable when they feel they are desperate.
Unless you have done something in the past to make him not trust you or to give him doubts about your reliablity, then I think he should trust you and back you up being that you're his wife and that's what a husband and wife should do for one another.
If he's having a hard time believing you, is there something you could do or show him as proof that you're the one who's telling the truth? Or, maybe if the situation doesn't allow for that (there is no type of physical evidence that could help you) then perhaps you can convince him to believe you until the ex can bring proof to the table about what she's saying.
He said, she said is a hard thing to deal with, especially without any proof.
I say, the ex needs to provide proof with what she's saying and if she can't, then your husband should not listen to her. She's probably jealous or has some sort of other agenda as to why she's trying to turn your husband against you. Try to find out what her ultimate goal is and what kind of outcome she's looking to get and nip it in the bud!
Hope this helped!