In sickness and in health. I wouldn't even consider leaving him if he had a more visable illness. That's why I feel like such a cow
The thing is, it's not the fact that he's got an invisible illness or a mental illness that's making you feel like you can't do it, it's the impact of his illness on you and your family. If he had a visible physical illness that was causing such an impact you'd feel the same! I get the sense you are so afraid of stigmatising or judging him you're willing to tolerate anything as you don't want to seem like you're not understanding. But you can be understanding, be completely knowledgeable about and respectful of mental illness, and stil struggle. It's okay to find it difficult. If he had a physical illness that affected you all so badly and there was no sign of it getting better and it was bringing you down you'd find it just as hard I think.
How long has he been with this therapist? As if it's longer than a couple months I would be encouraging him to have a discussion about how it doesn't seem to be working. Try something new. There are a couple of evidence based types of therapy within CBT, one more behavioural based and one mode cognitive, so perhaps it's worth trying something different? Or another therapist. Sometimes it's the therapeutic relationship that's getting in the way of progress.
What else does he do to manage his depression? Exercise, healthy eating, socialising, being active and engaging with hobbies? Does he come back from therapy with work to do between sessions? If he's having proper CBT he ought to be. It's not just about chatting and offloading, it's about setting goals and then learning techniques and strategies to help improve your mood and manage depression and reach your goals.
You sound like a very loving partner. It's okay to recognise this is hard for you too. That doesn't make you selfish or mean you don't care about him. Lord knows there are days when I'm at my worst my partner is frustrated with me or my mood brings him down too. He's only human so I get it.
Also I'd encourage you at times to try and focus on being his wife not his therapist, it's tempting to get super involved with his mood and discuss it all and try help but only he can take steps to change, you can be a supportive wife and let him know you're there for him but make sure you don't just fall into therapist/shoulder to cry on mode as that will seriously disrupt your romantic marital relationship, perhaps irreparably.