Each of us chooses our own friends, lovers, and spouse.
If his ex is the type of woman you would have been friends with had she not been involved with your spouse then you are being true to yourself if a friendship develops. If on the other hand the only reason you dislike her is because she was involved with your husband before you then you may be petty.
Most people have dated others before and not every ex becomes one's enemy. Recently I had a young lady complain to me about a guy she had been dating for 2 weeks who has remained friends with an ex for 12 years. I asked her if she really (expected) this guy to dump a friend of 12 years in order to please someone he's known for 2 weeks?! That's an example of an unrealistic expectation!
Personally speaking I'm not a fan of being with someone who is in constant contact with an ex unless they share a child together. In most cases we learn about such things early on. Therefore instead of forcing someone to change (their) lives it's on us to move on if we're unwilling to accept them for who (they) are and what comes with them. (friends and family)
Too often people will get with you and wait until their is an "emotional investment" and then suddenly demand you stop being friends with others or stop doing things you have always enjoyed. Some have been known to give their mates ultimatums! The great news is he's not keeping "secrets". If you don't trust him dump him.
Instead of trying to change someone we are better off finding someone who (already is) the type of person we want to be with.
There are only two ways to experience joy and peace of mind in relationships: we either get what we want or learn to be happy with what we have.