I'd not get too hung up on whether someone is an alcoholic or not. The word "alcoholic" means different things to different people and there is no one universal definition. I would say that your DH has an alcohol problem and, sadly, alcohol problems tend to get worse.
The depression he is feeling is quite likely entirely caused, or at least significantly worsened, by the booze. And even if he does have depression that is entirely unrelated to his alcohol intake he won't be able to deal with that depression until he gets his drinking issues resolved. Another possibility - if you start talking to him about his drinking and he then steers the conversation onto how depressed he's feeling, then the conversation stops being one about all the booze he's pouring down his throat.
Someone with a significant alcohol problem has two big fears. The first is the fear of how desperately dull, hollow and awful life would be without the booze. Make no mistake - that's a powerful fear. To someone with a serious drug/alcohol problem the thought of life without their preferred drug is horrifying. How can they possibly cope without their chemical crutch?
The second fear more complex. It's a combination of the guilt over what their alcohol problem has already cost them (money, friends, opportunities) plus the dread of what they could still go on to lose if they continue drinking. And there's the fear of being found out as someone with a significant alcohol problem because, if they are, they would be under even more pressure to stop drinking.
In general, someone with an ongoing alcohol problem will largely ignore the second fear in favour of continuing to drink. The first fear is more powerful and the second fear can be explained away as "Well, at least I'm not drinking first thing in the morning so I can't be that bad and so the really awful stuff won't happen to me".
Again, in general, it is only when what their drinking has cost them mounts up so much it becomes unignorable that they start to seriously reconsider. At that point they may appreciate the near-certainty that their life is going to go completely down the pan if they continue drinking and they then do something about it. Or not. Many never get to that point and just continue drinking.
You cannot talk someone into sorting out their alcohol problem. Their alcohol issues are theirs to deal with. All you can do is make decisions over what you need to do to protect yourself and those you are responsible for from the effects of all the booze.
Regular heavy drinking has a cumulative effect. He may well not be properly sobering up from the previous day's drinking before he starts again today. Over time this usually gets worse.
Drunks make poor parents as their emotions and their reactions vary hugely depending on how much they've had to drink. Children need consistency and firm boundaries and someone who's spending half the time drunk cannot provide that.
Drunks also make poor partners as their primary relationship is with the booze, not the other person. They will blow off commitments in favour of getting drunk. They will make grandiose promises to their partners that they won't get too drunk at this party, or they won't be hungover the next day, or that they've only had a couple of drinks... and it turns out that those promises are hollow.
It is common for someone in a relationship with a drunk to end up as the booze police, counting how many drinks have been consumed, searching the house for hidden bottles, checking the recycling for empties that have been sneaked out. I know I did. Damn-near drove me nuts.
I wish I could say "Right, what you need to do is x, y then z and he'll stop drinking." But I can't. It doesn't work like that. I can say that my over the last five years my ex's drinking has cost her relationships, our children, numerous jobs, most of her friends, her driving license, her health and all her money. She continued drinking through it all (well, more accurately, she bounced between sober for a few weeks and drunk).
More recently she has stopped drinking and has stayed sober for some months now. I don't know what triggered this and I'm really not that interested - her drinking is her problem to deal with. My problem is to protect myself, and our children, from the effects of her drinking.
I can give you some recommendations:
First, ignore what he says about his drinking and pay attention to what he does. He's drinking a lot and he's doing so pretty much every day. That he feels it's not a problem is simply his opinion. It's not the only one that counts. If he was raised in a family of heavy drinkers (as my ex was) then their opinion of "normal" drinking is hopelessly skewed.
Second, try to get hold of a copy of either "Codependent No More" by Melody Beattie or "Getting Them Sober Volume 1" by Toby Rice Drews. I think the latter might be of more immediate use to you than the former, but they're both good books.
Third, try to stop thinking about his drinking problem as something that you have the power to fix. You don't. There are things that you can do - that don't necessarily mean splitting up - that will reduce the effects of his drinking on your life. Either of the books above can help with that, as can Al-Anon (the friends and family offshoot of Alcoholics Anonymous) and one-on-one counselling. I got some counselling organised by my GP and it was incredibly helpful for me.
Good luck.