hi Tim. supposing you have Jan-Dec in F2 onwards (make sure they are real dates like Column B. format cells to mmm if you just want to see the month name), then try this in G2:
=SUMPRODUCT((TEXT($B$2:$B$15,"mmyyyy")=TEXT(F2,"mmyyyy"))*(WEEKDAY($B$2:$B$15,2)<6))

ps: putting your MS Off Ver is helpful for us to give you newer & more efficient formulas