OP I sympathize with you, but also with your husband. His work situation sounds very similar to my current situation -- down to the small irritating personal habits of the other person that drive you absolutely INSANE. It's funny how those little things that seem like nothing to everyone else become so magnified in an otherwise stressful situation.
I was like your DH for a while, coming home and unloading on my husband, until I finally realized it was the only thing we were ever talking about. And (like you have noticed) talking about it did nothing to resolve the situation, but rather just made me more and more upset about it.
I firmly believe in the value of a good rant, but if his situation is similar to mine, I finally came to the conclusion that venting was not helping, and I needed to try a new tactic. The reality is, he (and I) cannot control the situation, but we can control our response to it. For me, I have found it helpful to:
(1) Acknowledge and accept that work is a source of stress (mine is also a stressful field generally, and this situation just adds to that), so I have to take steps outside of work to alleviate that stress. For me, that took the form of ensuring I maintain a regular exercise routine, doing yoga/meditation, and carving out time durin the week to read and/or watch a mindless TV show. The key is just being able to turn my mind off (or focus on something else), so that I don't dwell on the stressful work situation.
(2) Forgive. I'm still working on this one. I have to accept that this person is never going to live up to my expectations, that the company is never going to do what I want them to do (i.e. fire him), and I have to live with it.
Anyway, that's my experience FWIW. Maybe the new job will work out for him and things will get a lot better!