Urgh. OP I'd be giving him an ultimatum. If by the end of his course of cbt you haven't seen certain changes (looking for a job, concrete stuff) you'll need to separate so you can take responsibility for your and your child's life. His mental health issues do not mean you need to stay with him. And I say this as someone with episodic severe depression. If I were to continue to be severely depressed without any improvement and refusing to do anything under the sun to improve it, I'd fully expect my partner to leave and want him to do so.
He's part of a family and that requires engaging. The only reason he's able to be the way he is is because currently he can do it and nothing falls apart for him. Child still taken care of, money still coming in, bills still being paid. I reckon he will only change when the costs of not doing so our weight the effort it takes to change.
Yes it's harsh but all of the loving endless support hasn't worked has it? He needs to either put all of his effort into recovery or management or you can separate and move on. I'm sure from how loving and caring you sound in your post you'd have been happy with at least some sign that things are getting better, not perfection. But the fact you're so sick of it and it's been going on for so long tells me you're not seeing any movement in the direction you need for him to be your husband and partner.
It doesn't help recovery for mental health issues to completely ignore your responsibilities for a sustained period of time. You're enabling him currently. I know it's out of love but it's not helping anyone. To PP saying they don't believe in enabling, look it up! It's a thing. If I was allowed during my worst periods by my partner to take to my bed, do no housework, bring in no money etc. It would have a negative effect on me. I'd start to feel even worse because I was letting others down, have no sense of achievement, be worrying about the relationship, and be sinking further into the sick role. It's actually good for anxiety AND depression to try keep things fairly normal as far as possible: with depression it gives less time to ruminate and offers more chance for positive reinforcement, and with anxiety avoidance merely sustains and maintains it. I'm aware I'm talking in broad terms and each individual situation does differ.
OP you're not a bad person. If he had broken all of his limbs and didn't work and refused to have a cast or a pot or attend physio and do the exercises and this went on for ages, you'd be within your rights to move on. At the end of the day you can leave any relationship that's not working for you and the fact he has a mh issue doesn't change that. It sounds like you've tried and done enough. At some point you need to think of yourself and your child.
It's also difficult to know what's his mental condition and what is simply him being him, before he developed this was he a good partner and father? Did he pull his weight? Contribute to the household? Work?
It might be worth bringing this all up now so he can talk to his therapist about it and they both know what's at stake here and what needs to happen, and what they should be focusing on in treatment. I think that's fairer than waiting until the end then springing it on him it's over. But whatever, you have to make your own decisions. He may be mentally unwell but you don't have to allow him to drag you down too. Being depressed or anxious doesn't magically exempt you from needing to take an active part in your own life or contribute to the household. He sounds very self absorbed.