If it were me, I wouldn't discuss his "recovery" with him. That's HIS job and if he is truly working it, you will see the results without him having to tell you anything.
There is something I've been thinking about regarding your situation but wasn't sure how to put it without sounding critical. I guess I'll just spit it out and hope you take it in the spirit it is given. It seems to me like you may have physically separated from your AH, but not much else has changed. You still talk to him regularly, he still comes over whenever he wants, stays as long as he wants, says and does whatever he wants while there, and pretty much just continues to be his same old self, but just doesn't sleep there at night. You still allow him to upset you and you still worry about him and the whole point of a separation is to allow you to focus on yourself and your children.
It just appears to me that you still have way too much involvement with him and that keeps you confused. What can you do to detach from his actions? Have you started al-anon meetings yet? I think you would learn a lot about setting healthy boundaries and how to maintain your own serenity regardless of what you AH says or does.