My dad was an alcoholic. He drank about the same amount as your DH, though he never had a night off. I know a lot of alcoholics (messed up family). There's no such thing as a functioning alcoholic. Whether they're holding down a job or not, they are terrible for the people around them. And only one of 'my' alcoholics stopped, and that was only when his liver packed in and he needed a transplant (not saying that'll be the case with your DH - these were chronic alcoholics and all normalising each other's drinking).
It's my mum I struggled to understand/ forgive for the longest though, since she never protected us, and kidded herself that all was fine because he was 'functioning'. You're already doing better than her by asking these questions.
So, I think what I'm trying to say is that in my experience, it's not your job to get him to stop drinking - you won't be able to, that's up to him. But it is your job to keep your DD safe. I don't mean (just) from drunken violence, but also from the fear she'll feel when your DH is drunk and unpredictable, and the guilt - because she'll feel all his drunk/ hungover moods are her fault - and the shame, when she finally realises that not everyone's dad drinks like that. And potentially the loss of her dad too young.
Sorry if that was really grim. You described the smell of stale drink on your DH, and even now - years and miles away from my childhood - that smell still makes my skin prickle with fear. Hopefully your DH just has a bad habit and will kick it soon - this can and does happen, and is far more likely than the situation I described! 