Impressions are made throughout life but, especially before age 7. I don't know why it is so but, it is. I never drank in front of my kids when they were young. One drinks and the other dosen't. To this day I do not consume alcoholic beverages in front of my grandkids unless it is a glass of wine with dinner. I mean A glass of wine.

I do have a weakness for Johnny Walker and fine scotch on weekends. I do limit my intake and sometimes I don't touch it at all. I look at it as a take or leave situation.
It sounds like your DH is drinking every night and if that is so then he has a problem and needs help. Staggering drunk is unacceptable at any time. One does not need to be falling down drunk to enjoy oneself.

Have a nice chat with your kids and then with the DH and see what can be resolved, otherwise an intervention with his parents may be necessary.

Good luck,