My standard answer to questions like this used to be a police procedural that’s an urban fantasy, i.e. “Law and Order FVU: Fairytale Victims Unit” but Grimm eventually arrived to fill that niche rather nicely.
So my new answer is an urban fantasy medical drama. There are a few novels, but I’ve yet to see anything on the big or small screen that features doctors and nurses trying to treat non-humans. As the major plot, that is, I do know there are a few incidental inclusions in shows about the supernatural creatures instead, like an ep of the British Being Human where a young vampire ended up being hospitalized.