My AH has not cheated in our 3 1/2 years together or ever given me reason to suspect such. He and I both share the moral code that infidelity is a TOTAL deal breaker. No ifs, ands or buts. We discussed our feelings on that issue before we were even married. As much as he is a drunk, I do trust that his feelings on the issue are very genuine.
He also does not drive or go out to drink. He is a home drinker, so I'm sure the opportunity to cheat has never really presented itself.