Is use of multiple bibliographies, especially with annotations, in a thesis, accepted?
I think the answer to your question is very dependent on your subject and the culture of that research area.  In my area, math, I've never seen an annotated bibliography as part of the thesis.  I've probably only looked at 15 or 20 theses, but I've never seen one.  In other areas (humanities and social sciences?), I suspect such a bibliography is more par for the course.