Needpeace6, I think the advice you have been given is very wise. Thing is, whether he is in true recovery and speaking to this woman only as a friend and fellow recover-ee, or whether there is something else going on, it's still inappropriate.
Pretend he wasn't an alcoholic, under what circumstances would it be ok for a married man to be texting another woman days, nights, middle of the night? That would be pretty much never.
Just because he is attempting recovery doesn't mean it now becomes appropriate, there are millions of recovering male alcoholics in the rooms of AA that I'm sure he could connect with. He could seek out an AA sponsor for himself, perhaps he could get a therapist.
Now, of course you are not his instructor and you can't actually tell him what to do, however you can make your feelings known and ask him to stop. He either will or he won't, that's up to him. All you have to decide is what you are prepared to do if he says no.
That's a boundary, for you, not for him. If he says no, I need to talk to her, then what, what do you do? Are you prepared to leave the relationship, to ask him to leave the house. That's pretty much where this sits right now, with you making that decision for yourself.