Is it possible to use P-MOSFET at the floating high side of a MOSFET driver?
There definitely are PN half bridge drivers, and a pmos for the high side is fine nowadays for not very high power applications, but you need to get the correct driver for it (some have the PN fets integrated, like the FAN7093).  

It used to be that they had much lower performance than their counterpart n-type mosfets, so the drivers were made to use n-type for the high and low sides.  N-type still have better performance because of their nature of using electrons instead of holes for conduction (electrons have higher mobility), but not as severely as before.  On the other hand, P-type mosfets don't need a charge pump.

Take a look at this application note from Vishay: 
P-Channel MOSFETs, the Best Choice for High-Side Switching 

An EE-Times article also talks about this:
A primer on high-side FET load switches