Only you know your husband best and are in the situation.. these are just some thoughts I had while reading through your posts ....
If it were a gal he met up with in a bar or at a party and they had a fling and that was that, never heard from again etc, that would make his contrition more believable to me.
But going to the woman you cheated you wife on with for comfort? Bit odd. Which leads me to believe he is begging forgiveness because he got caught. Different then feeling bad because he cheated.
Someone on your facebook, texting, IMing etc, isn't just a drunken mistake, it is something a bit more complex and involved to me.
Forgiveness is fine but he really needs to refocus on his sobriety and stay away from social situations which may lead to this stuff.
You don't need to explain or owe anything to the woman he slept with. Close the book on that and if he is closing it as well then GOOD.
He needs a bit of growing up to do. His actions aren't really about alcoholism IMHO.