Your question piqued my curiosity. It looks as though literature on teachers' attitudes toward elementary/high school students is more plentiful, as well as literature on explicit and implicit mental health attitudes of psychiatrists, doctors, nurses, medical students and social workers (e.g., Dabby, Tranulis, and Kirmayer, 2015, Explicit and Implicit Attitudes of Canadian Psychiatrists Toward People With Mental Illness; doi:10.1177/070674371506001006). Sources on faculty attitudes seem sparse.
One article I found (Kendra, Cattaneo, and Mohr, 2012, Teaching Abnormal Psychology to Improve Attitudes Toward Mental Illness and Help-seeking; doi: 10.1177/0098628311430315) did focus on a university population. But it focused on student attitudes, and from poking around a bit on PsycINFO, my sense is that more research has been done on the attitudes of university students than of faculty. But at least there doesn't seem to be a shortage of tools to measure stigma and mental health care seeking, etc. The Kendra study, for instance, used the Mental Illness Stigma Scale as well as some scales for seeking and receiving mental health help.