No sense doing it when he's drunk, he won't remember much. You can catch him the next day and confront him with empties (assuming you found some), but he'll probably say they are "old" rather than recent. The lying is just so disrespectful.
After realizing the lies were going on for months, I confronted my AH. In the end I realized the bigger issue was the lying he was doing to himself. Yes, it hurt and I took it personally, but I had to detach and begin to see the level of denial he was in. Confronting it made me see the light , I pray that one day he will see the light for himself.