If you can't use JodaTime, you can do the following:
Calendar startCalendar = new GregorianCalendar();
startCalendar.setTime(startDate);
Calendar endCalendar = new GregorianCalendar();
endCalendar.setTime(endDate);
int diffYear = endCalendar.get(Calendar.YEAR) - startCalendar.get(Calendar.YEAR);
int diffMonth = diffYear * 12 + endCalendar.get(Calendar.MONTH) - startCalendar.get(Calendar.MONTH);
Note that if your dates are 2013-01-31 and 2013-02-01, you get a distance of 1 month this way, which may or may not be what you want.