I am for you. However, I also know how difficult it can be to live with someone who is severely depressed. FWIW, I am very much in the 'should stay and be supportive' camp, but I know from experience that it is extremely difficult to continue being supportive when the person with depression is having a bad time. Unfortunately, there is little help and support for the person ( in this case, your DH), giving the support and at times it does become too much for them to bear.
Bearcrumble and Cheese, I mostly agree with you, but have you ever read any of the threads on here where it is the male partner who has depression? They are full of 'he's just using it as an excuse - bin him' and 'it's HIS responsibility to get it sorted and shouldn't be taking it out on you' type posts. I am in the middle on that. yes, it is the depressed person's responsibility to seek help and no, it is no excuse to act like a twonk. But, I do believe that part of depression is that you are not totally in control of your actions when you are going through a bad period. I know that our family had a very difficult time when our loved one was going through this. It still affects me now. It is at the root of a couple of family problems ( within the extended family)that are still not fully resolved. But it has made our relationships with the closer family even closer and stronger.
OP, is there anybody within the family who can offer support to your DH? I can understand that he has reached a stage where he has 'had enough', but you both need support, for your own sakes as well as the children. Maybe your GP can help speed things along with the counselling? TBH, our loved one was on about three different meds during their depression, but it was the counselling that actually was the road to freedom for them.