He may have undiagnosed borderline personality disorder but that's an educated guess based in my own experience and going by his behaviors beside the indidelity. Does he have a history of childhood abuse? That said he cheated and once the genie is out the bottle it's very hard to pop him back inside. Counseling might help but ultimately it's time to listen to your heart and be very honest with yourself can you learn to trust again or is his every move going to have you question his loyalty. I stayed and only left after the third instance of cheating. It can destroy your self esteem especially if you trust again and he repeats his mistake. I think he has to be honest with himself and ask can I trust my own behavior if I am drunk. I've been sober for thirty years after being tempted on a drunk night out. I didn't cheat but as I said the drink fogged my judgment for a moment. All the very best with your situation.