This is not only a tough one, but also unfortunately very common... a divorce is about the adults & the kids get dragged in.
Having worked therapeutically with children for many years, I would strongly suggest that your husband not get involved in the "mud slinging". I would suggest that he use redirecting phrases that reassure the girls that he loves them very much and looks forward to every minute with them. He can tell them that sometimes parents can't get along and say/do things that are hurtful and it is better if they don't live together anymore. Avoid telling them "the truth", but continue to reassure them that mommy and daddy hahd a very hard time using kind words and decided that it was better for everyone if they didn't live in the same house anymore.
His actions and continued support, love and involvement will be far more impacting than trying to refute a story. The good news is... they are telling him what mommy is saying, so the odds are pretty darn good they don't believe her. They are showing him love and affection and he is returning the affection.
Get a counselor involved if their willingness to interact with him changes or one starts to act-out. Otherwise, the kids don't need "the details" until they are much older, if ever.
For what it's worth, a very dear friend of mine recently had her divorce finalized. She found out that her husband had been having an affair that started the week after they got back from their honeymoon. She was devastated, especially when she learned that he had gone to "her house" to sleep after their little girl was born b/c it was closer to the hospital. Really- not kidding.
Will their daughter ever know this version of the story? I hope not. He's a crappy husband and a cheat, but he's a good dad. There is nothing wrong with editing when both parties said/did things that they regret.