When H/XH first dropped the bomb, a psychologist colleague/friend of mine said that research has shown that the prognosis for saving a M is better if two people can be in therapy together, regardless of how that therapy is directed. A skilled therapist can help the mentally unhealthy spouse to "discover" ways in which they contributed to their marital problems. I suspect in your H's case, the therapist will be able to figure out pretty quickly that your H is depressed and find a way to address that. ..........The problem is finding a good therapist and a pro-M therapist.
Glamgirl's personal experience is an encouraging example. I suspect that if you go to therapy with H, there will be backlash from OW.