The only drama that my husband watched with me and really liked was Nodame Cantabile, the cleaning scene won him over, due to his pedantic character he felt a connection with Chiaki, and he really enjoyed Stresseman.
I tried other dramas, but with no success ( Bloody Monday - he watched 2 episodes, same with City Hunter, I even tried to persuade him to Hana Yori Dango... I don't know what I was thinking...)
He promised me to watch Bridal Mask together when I will start watching it. I hope he will be more enthusiastic about this one.
If your husband is in medical field, I think you should try with Code Blue - for me it was a really interesting drama, characters seemed more real that usual in dramas, and he might relate to this one.
