Hi Violet!
Your story is similar to mine (I so wanted to believe my husband was "functional" but looking he really wasn't) We have been married for 10 years (together 14, separated a year & a half). We have a 5 year old daughter. I left him (then eventually he went into recovery. We are trying to work things out, but remain separated). I also understand how the consumption of alcohol might be culturally interpreted, being from a very international/multicultural family too. However, your husband's & your lives are being negatively impacted by his drinking. . .this, to me, is a sign. It really doesn't matter what we call it (alcoholism, alcohol addiction, alcohol abuse, alcohol dependency, "drinking problem"). . .you are troubled by your husband's drinking. So, it's a problem for you.
People who are functional (& responsible social drinkers) don't drink & drive. And they certainly don't get into trouble with the law due to their drinking.
You came to right place, Violet! There are many of us who understand (& are going through/have been through what you are going through). Please keep reading & posting. There are a lot of people here who have rich experiences & wisdom to share. I am learning a lot too!
I have recently started to go to Alanon on a regular basis (I wasn't too keen with it at first but again I am learning a lot from really caring, wise people who understand those of us who have family members who are addicts/alcoholics). I hope you try out a meeting or two or three! (I think the recommendation is to try 6 different ones).
You, your daughter (& your husband ) deserve serenity. I will be sending positive energy your way & praying that you & your family can get through your challenges, regardless of what you decide to do (leave, stay, enter recovery, etc.)
Big hugs!