.. I also need it to work for date ranges between 02-01-05 and 01-31-06,
so I can't limit it to just the year

Try it like this then, with explicit, unambiguous date ranges defined:
=SUMPRODUCT((A1:A4=--"2 Jan 2005")*(A1:A4<=--"31 Jan 2006")*(B1:B4=--"2
Jan 2005")*(B1:B4<=--"31 Jan 2006"))
Success? hit the YES below
--
Max
Singapore
xde
---