The doctor told you that the medications would not affect your sexual desire, but it would hardly be surprising if your depression affects your sexual desire. You've got a heavy workload, a lot of transition, and depression. Sexual desire does not flourish in such circumstances. Don't put yourself down, you're doing well just to get from day to day, right now. Tell your husband he's just going to have to start things for a while, and don't be apologetic about it. You've got enough on your plate.
You may have mom syndrome. :>)) It's hard to switch focus from running after kids to being a hot wife! I've had that myself. Some days I'm tired and running on fumes or ready to pull my hair out OR look like a bird tried to nest in my hair . . . my kids are older now so not as much but when they were young, whoa. I could be a hot mess inside and out! The house could feel very much like it needed to be burned because cleaning seemed overwhelming which does NOT help the mood, etc. And frankly, to this day, the sexiest thing my husband can do for me is to say 'honey, you go take a nap. I'm going to make dinner, clean the bathroom and vacuum the family room". Oh, be still my heart!!!! So, I do think that plays a role. What are the ages of your kids? Also, is there anything else going on? How is your mood? Any depression or anxiety going on (low level or higher)? Your hormones could be wonky. Both of those can decrease your libido. Both can be helped if you talk to your doctor. How is your relationship with your husband overall? Any underlying issues there?