My exAH was often depressed too, I want to say "go figure", given the enormous quantities of depressants he was downing and the behaviour he exhibited towards those he loved, but hey ho. Unfortunately, no matter how much effort I put into understanding why he drank, why he was depressed etc, nothing made any difference to his behaviour and drinking. Time to look after you and those kids.
I left, after a long time of vacillating, I wasn't sure when I did it that it was the right thing, I was scared and I asked initially for a seperation to give him 6 months to demonstrate that he could give up drinking and then we would see if our marriage could be worked on. I gave him 9 months in total, he didn't give up for a single day of that. We are now divorcing, it has been a long, sometimes difficult, but always better than living with him, process.
Go at your own pace, the job, selling the house, seperate housing don't all have to be done together. Small steps, if you feel in danger, are there local womens resources you can get help from about a plan to leave? if not, do you know your exact fianancial situation now? can you see a lawyer about your legal situation? do you need a week away with family or friends to rest and get your head together a bit before embarking on the practicalities? Don't try all of these things, they are just suggestions to pick one (or none), perhaps posting here is your "thing" for today: Pelican has really good advice.
It can all be accomplished, gradually, one foot in front of the other... (())
Welcome to SR!