Hi
If it was my OH who was drinking I would not even contemplate un supervised access. Your baby has no way to defend Her/himself. You would never forgive yourself if he fell asleep and smothered your little one.
Your baby's safety is the most important thing. Do you think that your OH would be able to concentrate fully on him/her if he is concerned about where his next drink is?
I personally think that you should let him see your baby if he is sober, I would imagine that at the moment that would be impossible, so be it, it's his problem that he drinks, not yours or your babies.
I don't have an ASTBXH but I don't trust his temper and caring skills enough for my 4 year old son to see him unsupervised. We have a contact centre near us and I have given him that option, but haven't heard anything from him at all.
Don't give in to your OH's demands, from what I have read on here he will try all sorts of mind games and guilt trips. BE STRONG, keep coming back for help and moral support on here.
It will get easier.
Right I'll get off my soap box now.
Welcome and good luck