How can I cope with a husband that is emotionally unstable?

Family therapy. Can talk about what uike about each other and what u don't like and how to change it. Or convince him to see his pcp for evaluation and work up.
Husband unstable. Talk to your doctor about obtaining counseling and/or support specific to your problem with your husband. E.G. If your husband is emotional because he is an alcoholic then join al-anon to learn about this disease and get support from a group. There are many types of support groups. Also there are faith based groups you can join.