I think there's a difference between "not desperately wanting to" and "actively wanting not to."
In the former, you might not especially be in the mood or wound up, but you're perfectly happy to do it. You may not have a driving need/desire yourself, but you're not opposed to it and you're happy to participate. Perhaps you might be in a take-it-or-leave-it place. You may have a desire to be close to your partner but your body isn't actively craving sex when you begin. Often part of the way through your desire escalates. This is fine, because it's something done willingly and happily.
In the latter, you actively don't want to have sex. It may repel you, for whatever reason, or your body or your mind might not feel up to it. Having sex would feel like a miserable chore at absolute best (and I can only imagine would feel like a trauma in other cases). You may feel pestered into it, or the pressure may be internal and you feel like you have to even though you really don't want to. The thought of it makes you unhappy. Having sex in this case is not fine, because it's done unwillingly and unhappily.
The former helps to bridge the gap between the timing of couples' desire patterns. Say you're in a good place and feeling fond, though not achingly sexy in the moment, but your partner is: that's fine. Chances are the situation will be reversed at times. You don't both have to be at peak desire every single time.
The latter is very deeply unhealthy. You shouldn't drag yourself to sex or make yourself miserable. Your husband sounds lovely, and I doubt he wants to make you feel unhappy in any way, perhaps especially through an act that can be used to express love.
I echo the calls to talk with your doctor. It's a very common side-effect of this medication, and some talk therapy might also help as well.