How can I help my husband who is depressed because of his obesity?

Therapists can help. Help connect him to a professional. Depression is best treated with therapy, cbt and interpersonal therapy are both well validated forms of treatment. Good news is obesity can also be effectively treated with cbt and is even more successful when there is a support system. Ask your husband how you can best be a support system. Perhaps as a walking or cooking partner, planning rewards, listening.
Both are treatable. A person who has depression and obesity has two treatable diseases. A single primary care doctor can start treatment for both problems, and specialists can be called in to help if needed. If the depression is severe enough to have suicidal thoughts or plans, then hospitalization in a psychiatric unit at the hospital is usually needed (one can call 911 for help in such a situation).
Encouragement. Be a cheerleader. He may need a weight neutral antidepressant, such as welbutrin to get over the hump.