Speaking as someone on his side of a relationship...
I think he's just always concerned for your general health and happiness. If when he asks you what's wrong, you say "nothing", and turn around and ask him the same thing, he could very well take that as a sign that you're trying to avoid the question and turn it back around on him. That may or may not be the case, I don't know. I do know depression can cause people to clam up and keep things in sometimes, which may be why he always asks what's wrong. Again, I don't know if that's you or not, but just that it's fairly common with depression.
I agree with turquoise, he is trying to be strong for you and do what he can. Your concerns about him and his job probably upset him, because he's more worried about health and happiness than he is about money.
"...But he won't talk about it. He has a crappy job, that he hates and he seems to be getting angrier and angrier. whenever I try to talk to him he just says, don't worry, just get better."
^This tells me exactly that... that he is extremely worried about you and just wants you to be happy, rather than worry about his job. Also, when jobs are stressful, sometimes talking about it really doesn't help. My mother used to come home and complain about her job daily, and it drove me round the bend. Where I'm going here, is that when he comes home from work, he may well just want to forget about it and cherish his time with you, which is much more enjoyable when you're feeling well
I hope this helps you out some. If he truly loves you like I get the feeling he does (as turquoise said, 10 years does say something), then his primary concern is YOU, not money. If you want to talk about it more, feel free to PM me. I'm sure we both could learn a lot more by talking about it
Good luck, and take care!
~TheDeliciousDish