He's right not to take psych drugs, they are SO bad for you!
I recommend Bach Flower Essence. The general one for anxiety and stress is called Rescue Remedy. It's 100% natural, non addictive and I think it works! You just put 4 drops under your tongue. You can't OD either. You can also put 4 drops in water and drink it, but it's less effective.
I also recommend a chiropractor. Sometimes physical pain translates into mental pain. The chiro can treat his back pain and anxiety stomach. You also might want to look into massage.
He needs to up his vitamins. I recommend Alive brand for Men. A good dose of Vitamin B-1 may help with mental stress.
At night, avoid TV since TV stimulates the brain. Avoid sugars and foods with food coloring and preservatives. Have him sleep in a cool, completely dark room. Studies have shown we get better rest in completely dark room. Cover up the clock light as well. Sleepytime Tea is good for sleeping.
I also suggest, instead of having him go for anxiety, have him checked for food allergies. Perhaps he'd be willing to do that? Food allergies gave me the same symptoms you just described. They came on during a time of stress in my life so I didn't realize what was happening. I never had the allergy before, but I had horrible acid reflux, I couldn't sleep, I couldn't eat, I couldn't drive without panic attacks, I felt like I couldn't breathe and I literally wanted to crawl out of my skin! The doctors were close to prescribing me a host of psych drugs like Xanax when I broke out in a rash. I went to the doctor for that and he prescribed allergy tests because the rash wouldn't go away. Turns out I had a bad food allergy to milk and eggs (which I never had before.) I eliminated the foods from my diet and all the symptoms disappeared in 4 days. So it's worth checking out. Believe me, I could have been on Xanax for life, never knowing it was eggs and milk! Tell your husband the story, he may be willing to at least get checked.
Good luck!