PBS is the "all purpose buffer". In order to avoid unspecific binding add BSA or Tween-20 (ideal concentrations vary). If you do not have staining for particular antibodies: how do you know that the antibody works, at all (positive control for IHC)? How do you know that the antibody works in your particular staining (a particular fixation might destroy the binding site of the antibody (epitope) or makes it inaccessible)? On the other side, soluble antigens might get lost without fixation (washed out).
The antibody is reactive for both mouse and human tissues. It is already working for the mouse but not for the human tissues. I thought that the positive staining of the mouse tissues can be considered as positive controls of this particular antibody for the human samples.
I usually use a 1% milk blocking solution with 1%DMSO in PBS to incubate antibodies, this has always worked well. However not sure that this will help in your case as this generally helps to reduce non-specific staining, not make staining stronger.
TBS (0,25 mM TRis+125 nM NaCl, pH 7,5) is a good buffer, you may use BSA (1-5%) in the incubation buffer. If you have trouble getting signal i human tissue try antigen retrievel (try boiling the slides for 40 min in 10mM citric acid, pH6,0 using NaOH 0,1N; you may also use microwave oven but for aprox 12 min)