I tentatively tried the COUNTIFS function spanning across sheets. It did not work. To double check, I did a search and came across this thread which confirmed my suspicions:
http://www.excelforum.com/excel-form...le-sheets.html

So, the pointers are:
You cannot use the sheet spanning feature on COUNTIFS
You want to use COUNTIFS and not COUNTIF
You could have static cells in each sheet which perform the COUNTIFS for each sheet and then on your 'main' sheet just sum up those cells (using SUM with sheet spanning if you wish)
OR you could write a formula in your main sheet which performs a COUNTIFS for each of your monthly sheets (i.e. COUNTIFS(jan...)+COUNTIFS(feb...)+...+COUNTIFS(dec...)
OR you could try that suggested named range trick suggested by vlady in the link, but I did not confirm that would work