Understanding Class D Amps

checking low side gate drive is easy done using a standard probe. You can even measure hi-side gate drive with a standard probe applying a simple trick: Disconnect all hi-side drains from the supply and then you short the bridge outputs to GND. Now hi-side gates are referred to GND, too, and can be measured with the standard probe.
Btw - HIP4080/4081 is a beast that after years of use blew the MOSFETS of my first DIY-pwm-amp powered by 12V SLA - never used them since.