Hi Laugh. I hope I can be of some help here.

I think you're doing just fine by assuring him as you are. Keep in mind, as he sees himself now as a result of his depression, his self esteem and sense of self worth are rather low. Thus, he can't see himself offering anything for you. This will likely ease in time as his depression eases (you mentioned a medical staff, so I am going off the assumption he is getting help), but you can help him by just being there for him. To me, it sounds as he does genuinely love and care for you. I think, when he looks back on this in the future, he'll realize how lucky he was to have someone like you to help him through this. You just need to do as you are, and be patient with him on his off days.

Just remind him that beside him is where you want to be, not where you feel like you "should" be or where you are "trapped" at.

I hope I was of some help.