It will depend on your setup but if you are the default setup for the English version then this should do the trick.

SELECT datepart(mm,cast(replace(birth_date,'.','') as smalldatetime))

Note: 'dec 12,2004' is understood as 12/12/2004. But 'dec. 12, 2004' will cause an issue. As long as all are the standard abbreviations you should be fine except needing to drop the '.'.