You sound ever so down on yourself. I am sorry you're having such a bad time right now.
It is hard to live with a depressed partner, no question about that. If you have prolonged downs, your partner can sort of 'catch' it - which is something he needs to guard against. He can do that by making sure there is joy in his life. When two people love each other and share their lives, there's a tendency to take on each other's feelings and feel responsible for them. There seems to be a bit of that happening with you two.
If your H tries to 'share the load' of your illness with you, it doesn't help you: only makes him depressed, too! Likewise, if you expect him to understand how you're feeling, you're asking him to feel depressed ... On the other side of the same coin, you can't decide for him, whether he wants to stay married. He says he does, so believe him. And you can't be solely responsible for the amount of joy in his life; he can find it with your children, at the gym or whatever he does, and in the small things that do bring joy. (One of mine is going through a car wash, but let's not assume I'm typical 
)
YOU are still in there, under the depression - the you he fell in love with, whom your children adore, and who makes it through the day even when it feels hard. It might be a reasonable idea to talk about this (temporarily) hidden YOU with him, and put some of theings back in your life that let you express your happier side - even for a little while. Are there some films you both find hilarious? Have you stopped dancing round the kitchen with the DCs?
Read the book, please, it sounds like he needs a good listening-to and this is why he asked you to. Go back to your doctor and/or therapist if you're feeling worse.
Find one little thing to revel in every day, however tricky that might seem sometimes. And trust your husband when he shows he loves you :) Good luck xx