I don't know about the driver but i wouldn't recommended you to use this circuit,because of the way you have connected the two gates together.
This prevents you from being able to control the 2 mosfets individually and you will have periods between the transition of the mosfets where both of them will be conducting.
The proper way to drive an H bridge (or half) is to shut down the 2 diagonal mosfets and after a small delay open the other two so that the 2 mosfets in the same side never work simultaneously.
Alex
---------- Post added at 00:11 ---------- Previous post was at 00:08 ----------
The second problem in your schematic is that if you drive the gate with 15v then you are over the 20v Vgs limit for the N channel mosfet
and when you drive the gates with -15v you are over the 20v Vgs limit for the P channel mosfet.
Going to any of the major old-line power management
semiconductor companies (TI, IR, Intersil, etc.) and
entering "half bridge driver" in their Search window
(you have heard of the concept?) would give you hours'
worth of options and information. Application notes can
be an especially compact education.