Deapression and anxiety can go hand in hand as in your husband's case. It seems like both of you are experiencing a lot of changes in your life and the transition into fatherhood can be very difficult for some men. Hang in there!
Your marriage is not over, it is just going to be something you both are going to have to work harder at.
Especially with a newborn, one can neglect their relationship with their significant other. You just have to be more aware of this knowing his vulnerability in his mood.
Just don't give up okay. If he is willing to work on his issues that is a great sign!