I don't think it really matters whether he's a functioning alcoholic, or a problem drinker or gets fall-down drunk everyday. If his drinking is a problem for you, it's a problem for YOU. But it's not a problem for him. And you can't make choices for him. You can't control his drinking. You can't make him stop.
But you can set boundaries for yourself about the kind of behavior you will accept around you and your children.
If you don't like that he drinks around your kids constantly, you can say, "I think it is harmful for my children to see you with a beer in your hand 24/7, therefore, if you are going to drink, don't do it in our home or around are children. If you do, I will be forced to reconsider this relationship and our living arrangements."
Of course it's up to you what you do and that is just an example, but never draw a boundary if you aren't willing to follow through on consequences...
Al-anon meetings would be so helpful for you.