I have watched the show a few times and I actually like it now but it does not seem like a comedy to me at all.
I just want to know if the show is a comedy or if it is a drama. 
It’s drama-com. Comedic drama. Just like Monk or Ally McBeal.
Well, based on last night’s (13 Dec) episode, you got comedy: when John’s mother thinks that he’s bopping Susan and tears her dress in a cat-fight, or when Wossname tosses the blender into the grave My biggest laugh, however, was in the opening sequence, when Gabriella is in the hospital, pondering the emptiness of her life, talking to and watching the nurse, and sees that she needs to help others and we think she’s thinking about a career in nursing, but she’s thinking about holding a charity fashion show. I cracked up completely.
… and and you got drama: when the kid pours out his fears that he’s killed his sister
It’s an interesting hybrid, both a soap opera and a parody of a soap opera. (The first episode, BTW, was hilarious, but subsequent ones have been less funny – though with some fun moments.)
C L – you forgot the funniest bit from the opening:
When there’s a problem at the fashion show, Gabriella uses the same dialog the Nurse did when trying to save the patient
According to the Golden Globes, it’s a comedy.
I had the same thought as the title of your OP when I heard it was nominated as Best Comedy and/or Musical.
The plots and situations are classic sitcom. They just kill a lot more people than most sitcoms do.
Soap had a decent body count.
The Golden Globes didn’t decide it’s category, the network did. It’s considered a comedy because ABC’s other big popular show, Lost, is definitely a drama and they didn’t want them competing with each other for awards.