Jquery data table column filter header responsive
Solution 1:
Complex headers are not supported with Responsive plug-in 2.0 and 2.1, see this answer for more details.
The workaround could be to rollback to version 1.0 until author releases a fix.
Your HTML markup is incorrect, you should use single thead with tr for each row and th for each column.
See corrected example for code and demonstration.