It is obvious he is experiencing depression, but being compassionate to this does not necessarily mean accepting that he can't do anything about it. I have an ex husband (not a survivor but other mental health issues) and he didn't work or do anything to help around the house etc. I was constantly afraid that if I pushed him or left he would just end up taking his own life (and he threatened this a lot). Yes, I do have a history of co-dependance! Anyway, I eventually ran out of steam and completely fell out of love for him. When I did finally leave after 7 years of this he got into his doc, got meds, went back to school and has had the same, stable, good paying job for the last 14 years!! Point is, if your H didn't have you, do you think he is so sick that he would have allowed himself to be homeless or institutionalized for depression? Likely not. He doesn't take care of his own living needs because he doesn't have to. If he can't work a job that provides income for the household, then set the boundary that he must still work - work on running the household and on himself so that he can one day be an income provider again, but the option to not work is off the table. You are not controlling him and ignore these protests. You are simply relinquishing your role as his caretaker and mother. He has to put in the time or the money. Period. Set the boundary with time limits and know that as much as he tries to manipulate your emotions to stay stuck in his safety zone, put on your steel jacket and just keep saying to him "this is your choice... you can choose to work on yourself and on your family, work for money for your family or provide for yourself on your own". But those are the only options. You are actually doing him no good taking care of him and allowing him to stay in this place of depression and non-living.
Good luck. I know it is hard, but remember you are doing this for you, for him and for your kids. Everyone wins, he just doesn't know it yet.
I am not your rolling wheels, I am the highway
I am not your carpet ride, I am the sky