In my opinion, stopping drinking is not the way to "pay" for the mistake. You should stop drinking because it's the right thing to do for you. Cheating and drinking often happen simultaneously, but are not the same thing. Do you tell? How many people in your shared life know about the incident? Do any of his friends or common friends know? I am a big believer in not disclosing what won't come back to bite him, especially if you are resolved to learn from the lesson.