For the eczema, I would recommend a good probiotic. My son had severe eczema, and when we found the right probiotic, his symptoms reduced within 2 days. Didn't clear up, but hey, using less steroid cream is always a good thing! I could say a whole lot about getting rid of eczema naturally, but I think I will settle for sending you to the blog I wrote about my son's experiences: http://mybabyhaseczema.com Granted, your husband isn't a baby, but there are many things that apply to any age, tests you may want to ask his doctor about, etc.
If you can find a naturopath, he or she will probably be able to help you work up a nutrition plan. He would probably run some tests to see if you are deficient in any area, and then supplement specifically for that, and/or recommend foods that are rich in the nutrients you are lacking. Of course, a good Vitamin B supplement (meaning injection or sublingual) could be helpful with the depression.
Dr. Neil Nedley runs a very successful depression recovery program. You can check his site, http://www.drnedley.com/, to see if there are classes in your area, or to get more information. He is an MD that has chosen to follow a much more "wholistic" approach to medicine, which includes things like diet and nutrition. I think you would learn a lot from his site.
I personally take vitamins. I have taken various kinds over the years, but have only noticed results with two. One is Vibe, from the company Eniva. It costs about $50 for a month's supply of the liquid vitamins. Now, I take Melaleuca's Vitality Pack, which costs about $20 for a month's supply, is in pill form (small pills, too), and I get the same results or better. What results? More energy, even when I am sleep deprived. More emotional stability. That one is big. My husband doesn't like it when I have a melt down, and as long as I consistently take my vitamins, I don't seem to. The reason seems to be that these two vitamins have a very high absorption rate, as opposed to pretty much every other vitamin on the market.
Speaking of Melaleuca, they make a really great lotion that also made a difference in my son's eczema: Renew. It's the reason we started using Melaleuca products--I had to get it, because I could see results, and it was the first lotion or cream that I had ever seen noticeable results with. Then I tried the vitamins and the cleaning products, and, well, I was hooked! Not that I'm trying to sell you on them, but if you know someone who gets their products, you might ask about the Renew and the vitamins.
I could go on and on about nutrition and diet, but I think that's a good place to call it quits. Check out the links, and good luck!