N-channel and P-channel mosfet for inverter
No, the P-FET is not connected correctly.  You need 10V Vgs to get the specified on resistance of the 9530.  When your input square wave is low you expect the P-FET to be ON, i.e. the source close to 0V.  However, if that were true Vgs would be zero.  So you have a source follower configuration where the source voltage will hover somewhere around Vgate + Vth.  You're better off getting a controller IC that has two outputs for driving 2 N-FETs in this topology.

Take a look at something like the LM5033 from TI: http://www.ti.com/lit/ds/symlink/lm5033.pdf