Hi Beach, it sounds like you're really going through a tough time right now. Sometimes it's not actually the person with depression who suffers the most, it's the person who has to take care of everything for everyone. It's incredibly draining and emotionally exhausting, and your husband needs to acknowledge that. Having an illness like depression doesn't mean you get a free pass from the impact on your family members; just the opposite, you need to appreciate the work they do to make sure life is as secure as possible.
I was worried when you said you didn't want to burden your friends. Beach, that's what friends are for. We have friends literally so we have a support network for when things are bad, and so we can support them when they need us to. If the situation was reversed, are you telling me you wouldn't be horrified by the fact your friend is struggling and didn't want to tell you because she didn't want to be a burden? A cup of coffee, a slice of cake and an hours talking can lift an incredible load off your shoulders. Don't be afraid to ask for help, it doesn't mean they would feel burdened by it, it just means they would listen and maybe have some thoughts or suggestions, or just even be able to relate.
A while ago, I went through the worst period of depression in my life, I was at suicidal levels. The only thing that got me out of bed in the morning was my dog needed to be walked. I essentially loved him more than I hated myself. And then once I was up, I forced myself to go to work, etc. Got through the day, to do it again.
The point I'm making is, try asking him to go to see someone again, but instead of doing it for himself, do it for you and the kids. Because at the end of the day Beach, you may love him, but he needs to take steps towards managing his illness as well, and that means exploring all options that could improve his quality of life, AND yours, and that includes talking to a professional. If you're in a family unit and you have depression, then it is not all about you, it is about the family unit. Because you are all affected.
It sounds like to me you're just absolutely exhausted, drained, and wondering if life is ever going to improve. I can't give you an answer to that unfortunately; all I can say is that if this man isn't willing to try absolutely everything to keep someone like you in his life, maybe you should try separation even just to give yourself a break for a while. I hope life improves for you.