You, BlondieQT1, have the task of transforming yourself into the better option. It's really as simple as that, though not easily done, and certainly, there are no guarantees. Assuming he's not a sex addict or has some psychological problem that gets him cheating, your contribution to the relationship has combined with his to create a relationship whose influence on H was to make him unhappy, and he decided to deal with that by looking outside the relationship for a fix.
This isn't a matter of whether he's wrong in so doing, BTW. He is, but it's not a perfect world populated by perfect people, so those arguments are futile and only serve to make the individual arguing thus feel morally superior. It's like a self-inflicted gunshot victim, an attempted suicide, comes into the ER. Are you going to argue about the morality of suicide, or are you going to do what you can to fix the situation?
Same goes for whether he's broken your trust (of course he has) or whether he chooses to remain friends right now with the OW. that's NOT your big problem right now. If he wasn't "friends' with her, he'd be "friends" with someone else. I don't mean to sound cold, but, hey, we've got a patient in ER and we need to work stat. Are you willing to focus on what you need to do, rather than on what he's doing?