Where do English/History or Humanities professors post their research publications?
It's possible that this question will be closed as a "shopping" question, but I'll try to provide some general information.

In the humanities and social sciences, scholars have been slow to adopt the practice of putting preprints of articles up on the web for other scholars to read.  There are some preprint servers for various areas in the humanities and social sciences, but these are not nearly as heavily used as (for example) ArXiV is used in many areas of science and mathematics.  

A further issue is that much of the scholarship in these disciplines is published in the form of books rather than articles.  For example, a typical expectation of an assistant professor in these disciplines is that they publish one book out of their dissertation within the first few years after the Ph.D. and have a second book published before the end of the tenure period.  Publishers of scholarly books in the humanities are mostly unwilling to allow the authors to make versions of the books freely available.  

In my experience, Google Scholar does often include journal articles in the humanities and social sciences.  Furthermore, it's quite common for the web pages of faculty members in these disciplines to list their publications.  Thus I'm surprised that you say you can't determine what they've published.  Are you saying that you can't find any information about what they've published, or are you asking why you can't find freely accessible copies of this material?