Personally, I don't see this as cheating.
It also sounds like your husband is slowing down your relationship with your bf out of envy. It sounds like if his relationship were going faster, he would be ok with yours going further with your bf. If you and your husband were mor established, then I would say he should look at his envy and think about it. However, since he is still coming to terms with stuff, then I think some leeway is appropriate.
Sounds like there is a lot going on with your bf. He needs to figure out what he wants. If he sees his ex-girlfriend as a friend, then he should trust her with the truth. If she doesn't like him because of that, then was never really a true friend.
Good luck to ya.