Sympathies, that sounds hard and no I don't think you are UR for finding it hard having to listen to his stresses for endless hours whilst also working yourself, running a house and small kids, I think anyone would find that hard.
Couple of random thoughts, may or may not be helpful
-Have you asked him whether he's actually finding these long moans helpful to him in destressing/decompressing or whatever? DH and I both have jobs that can be stressful (in a different way to teaching) and although we do of course talk about work sometimes I don't always actually like doing so, as we can end up circling a topic over and over without coming to any kind of resolution or just winding one another up and doubling our stress rather than minimising, so we have a '10 minute' rule for work chat which is that if we've been talking about work for more than 10 mins at a time (informally enforced, we don't have a timer or anything!) we change the subject. He might actually welcome something like that as you can get trapped in a conversation and not know how to politely exit it, if with your spouse?
-Is teaching what he really wants to be doing in the long run if he finds it so stressful? I know it's the kind of profession you can get emotionally attached to and can be hard to escape but really there's no prize for martyring yourself and ruining your health/family life for what's just a job at the end of the day. Maybe he might not be able to immediately retrain or change jobs while you have young kids but making a plan to be executed even in 3-5 years time, working out the logistics and finances and having some clear goals might help? If he doesn't know what he really wants to do can you encourage him to do some things like career quizs/psychometrics online to identify what he enjoys/is good at, search threads on here and other forums (lots of posts about life after teaching), maybe even speak to a career counsellor, anything to feel like he's taking some control and ownership?
-You say you think he might be depressed, have you voiced that thought to him? I would encourage him to speak to his GP or to OH at work, people can be afraid of seeking help and perhaps are afraid of ending up on heavy medication or something but the ball will remain in his court, they may be able to recommend some self-help things that again will help him feel more in charge of his own emotions, there might be counselling or other support available through work, and if he is depressed medication can make a huge difference so it's worth thinking about?
-On the same note, a lot of people I know in stressful jobs do develop good techniques for unwinding after work and it doesn't all have to involve unloading on your spouse. Does he do any exercise or spend time outdoors, I know it's hard with young kids but if he could even get out for a walk or cycle or run for 20 mins a day I bet it would make a difference to his mood (you should have the same opportunity too!). Is there anyone else he can talk to about his work and life in general, family, friends, colleagues? Again, I know hard with kids but having social time is really important to a lot of people so maybe 'ring-fencing' time for a weekly drink after work or video call with his family could be helpful?