Hi OP. First I am really sorry you are suffering so much. Life sounds pretty hard for you at the moment.
With reference to your DH, I'm with Joysmum, Silvery, Matilda but also Almost.
I'm in a similar situation except with one toddler and no pnd (not to say I didn't struggle as the year we had DC was eventful to say the least).
I have been waiting for a break (holiday? DH to do much, much more?) since I became a mum. I was getting more and more exhausted and annoyed and started laying on the line what I needed from him. He accepted it all and got a bit more helpful. I didn't think it was enough. It wasn't- I was doing nearly everything domestically, household management wise, routine childcare/ arrangements for paid childcare as well as working part-time. I'm not denying that I had let balance of domestic duties slip long before we had DC and my husband has in the past put things off/ expected me to do it.
However I suddenly realised that my grievances were not the priority any more because DH is burning out. Not just complaining about work but sinking. My current job can be stressful and I have responsibility but I enjoy it and have professional confidence. But I have also had horrendous working environments where I had to steel myself before I could go in each day, where I felt completely trapped and often paralysed with worry. There is a difference between day-to-day job difficulties and this.
The latter is what my DH is experiencing now but unlike me, when I was experiencing it, he is responsible for paying a mortgage and putting a roof over three people's heads. He's also well aware that if he passed the baton to me for a while, even if I worked full-time at senior level, I could not make the amount of money that our mortgage is based on.
My DH taking a job with less responsibility would be great. But at the moment he can't think straight, he certainly doesn't have mental space or actual time to research and apply for other jobs. He's lost confidence in himself. He has anxiety and depression, this has crept up on us and we've only just acknowledged it between us and with confirmation from his doctor. His mental health is now the priority even if I was still annoyed with the unfairness of what I am taking on- it has to be shelved for now. Obviously I have no idea OP if this is the same with your DH but if it is anything like my situation it is neither fair, useful nor appropriate to tell him to 'man up'.
I also question whether one can tell someone what they need to do in their career, especially if the career is one that you have no understanding of and especially if the person has anxiety/ depression. Again, this may not be the case with you and your DH, OP. But even when you understand someone's work environment very well I still wonder how much instruction you can give someone about how to do their job. Saying 'delegate more' - is that helpful? I have been guilty of doing just that but surely he knows he should be doing that but just can't see a way of doing it. A bit like when someone tells you to calm down.
The suggestions Joysmum gives are more useful as they involve questioning and working together so if you have that kind of relationship you might help your husband make headway. It gives him more of an opportunity to work through the barriers and possible solutions in his own context rather than someone throwing generalised work instructions at him. I think I might try some of these myself but these things have to be tackled gently so that someone who is really struggling doesn't feel even more overwhelmed. It's also a useful suggestion of Almost to look at a time management course and yes I think in the future it would be a wake up call for many men to play out what the mother's of their children do on a day to day basis. But not now if he is at crisis point.
Of course none of the above might be the case with your DH. He might just be being a lazy git! He surely isn't giving you the credit you deserve for all you are managing. However in my case it flipped from me telling DH he had no understanding of what I was doing to realising that he knew I was doing thousands of things and felt like a failure for not doing 'his end' of the bargain.
So whether or not your DH cannot or will not support you at the moment, it might be useful if you can do the following for yourself:
Speak to someone trusted about what you are going through to get it off your chest. I can see that getting your own counselling could be financially and logistically difficult at the moment.
Ask for as much support as you can from friends and family. Do you have an practical friend? Ask her/him to help in this way. Do you have a wise, empathic friend? See if she/he can meet you for a walk around the park etc. Do you know someone who has experienced a similar thing? Speak to them or see if your DH wants to speak to them. Do you know someone who is good with your kids? Maybe they can take them for a while while you have a little time to yourself.
Read up on depression/ anxiety in men to see if that looks likely with your DH. It might relieve some of your understandable anger towards him. If this is what it is!!
Go to the doctor with your DH. Taking some control of the situation might help you both.
Try and breathe.
Sorry for the vast ramble. I'm knackered!! Take care OP.