Is it possible to use an H-bridge IC as dual MOSFET driver?
Only if  both external MOSFETs are low-side and only if the external MOSFETs have significantly more gate capacitance than the MOSFETs in the H-bridge IC. And since the MOSFETs in the H-bridge IC already have more gate capacitance than the typical input capacitance of a gate driver it will be slower to begin with.
And only if both MOSFETs don't have to be on at the same time since the L9110 doesn't allow that which you can see from looking at the truth table. This last one is probably a dealbreaker.