When is my biennial flight review due?
Yes. Your interpretation is the correct one. Several FAA legal interpretations cover the "calendar months" phrasing; the best I could find was the Harvey interpretation from 2012:


  Based on the facts that you have presented, a biennial flight review accomplished on April 2, 2002, would not lapse until May 1, 2004.


Basically, your flight review is legal until the end of the month (ie, June, or August) it was completed in two years before. The same calendar logic applies to maintenance like the annual inspection.