In my opinion, it may actually help things for you both to have medical problems. I have Crohn's, arthritis, etc. and my husband has spinal stenosis and degenerative disk disease. Until I had the arthritis, I didn't really understand when he didn't want to go do things because he hurt too bad. I completely understand now and we are both content to just sit on the couch or take a nap some days. We have a much greater understanding of what each other is going through. When I'm sicker, he helps me and it takes his mind off of his back. When he's sicker, or recently, he got injured and I had to do almost everything for him, it took my mind off of my pains, which was really nice for a change.
It will definitely take some adjustments, but this may end up being what he needs to come to accept his own problems and get on the right meds. If you talk to him about it and let him know that you need him to take care of himself now that you have your own problems to worry about, you might find that he will indeed step up and do what he needs to do. My husband used to avoid drs, meds, etc. for his back, but once he learned that I do rely on him at times now, he started being much more responsible and got on different meds, got different drs, treatments, etc. Best of luck to you. It's not easy and anxiety meds definitely help, but it can be done and it can work to both of your advantages for you both to have an illness.