Also, you might want to read and compare the stories of all the wives and girlfriends who gave the alcoholic one more chance on this forum.
In a similar way we did this with my Mom. It was me who spent a lot of time and energy and unhealthy codependency getting her or attempting to get her the help she needed.
First time we got her into a program it was wonderful. I thought this was it. She actuallly did not drink for a while.
Then one day, when visiting her, went to the garage and found one half empty cold beer. I went bonkers calling other family members wanting to know who had bought this, huge fight. It was awful - she did not want to stay sober. And I had worked so hard to get her sober.
I stayed away for a bit but then would come around and help her around the house and there we were back to square one.
Then I exerted more energy on other plans to get her forced help.
I know how truly painful this is.
Other members may correct me here for this advice which is not taught on this forum:
Let him know he is being left out of the house, find out if he gets a job or goes into a program, gets help for his depression, etc and then take him back in. Don't go to the "he's going to be homeless under the bridge" just yet. That is causing you a lot of worry.
This is your decision, but if it causing you so much angst and worry - just assure yourself you won't let him be homeless - for now - to get some peace.
Then read the stories, post on the alcoholic thread, read books. There are a some good stories, but very likely you might be back at square once again in a few months. And that is where you find out how this becomes a mental health issue for us the enablers.
Since this seems to be happening right now for you I believe I read that meetings (such as Alanon) are not feasible after your work day - they might have online Alanon that could help you deal with this.
You are at the point where you have made the decision he is out of there, hopefully you will be strong enough to stick to that for now and go through with it, but if not at this time you can at least temporarily (don't tell him this though) demand he leave and find out if there is any interest in progress on his part after he is out the house and facing the reality of his situation.