I agree with everyone else that your husband is definitely depressed, whether his medical condition and/or medications brought it on or just made it worse, he's depressed!
The first thing you need to do is to get him to address this and depending on his medical problems, it may be more difficult. Depression hurts the whole family, especially your children.
He also needs to be the full-time care provider for your children, unless he is physically unable to do so because of his surgery. If you are uncomfortable with having him do this, you will need to look at the reasons why. Is it because you can't get him to get out of his room and function as an adult? If so, and for many similar reasons, treating the depression should improve this. If treating the depression doesn't resolve the issues, then you may want to run. Also, if he is not caring for the kids, he needs to be working (assuming he is physically able to do so), no matter what his background is, he can seek work through a temp agency if there are no full-time jobs currently available.
Finally, I think it would be good to see a marriage counselor. I think he needs to take steps probably through counseling AND medication to treat his depression and rejoin the world, but if that doesn't improve the day to day interaction between the 2 of you, you maybe should consider seeing a therapist together. They can help teach you new ways to communicate without him turning everything around and making it about you.
It is very hard as a mother being the primary (or sole) breadwinner, and being the lioness fiercely defending her cubs (although that one comes naturally), and to feel guilty about not being the one caring for them, and not trusting anyone to do as good a job as you could if you didn't have to work full time, and to have the financial pressures of being the one working full time, and to make every single decision in your family's life, and on and on. Men, at most, have half of these pressures (unless they are a single parent). Although, they may replace the pressure with feelings of inadequacy if they are in the role of caregiver instead of breadwinner. You have a lot on your plate, especially with twins, you need the support of your husband. I hope you are able to convince him to seek help for his depression. As one of the other mamas said, maybe you could speak to his dr and have the dr adress it at his next appointment (assuming he has frequent checkups).
Good luck!