I use this two condition on the date I'm testing against.
=EOMONTH(TODAY(); -1)+1
and
=EOMONTH(TODAY();0)
The other method to test for the date is not taking into account the year and would get you the data from the past years.
You would need to do the following, which is longer.
=AND(YEAR('Date')=YEAR(TODAY());MONTH('Date')=MONTH(TODAY()))