Just because he's attending meetings, doesn't mean he's actually working on his recovery. Just like AlAnon, the people at the meetings are there to offer their experience, strength, and hope. They're not going to tell him what to do with his life. If he makes the choice to cheat....that's on him. Just like his choice to drink is on him. No one holds a gun to his head and makes him do either.
What are your boundaries? If he cheats, then you take him back as soon as the gf leaves, what is your message to him? Marriage counseling is a good idea IMO, but only if you're both committed to the marriage. It won't work if he's not taking accountability.