I recommend making two changes: reduce the gate resistance and add a diode across the gate resistors. 100R resistors may be a bit too large, so try 10R or thereabouts. Adding a diode to help discharge the gates of the MOSFETs also helps turn them off faster. Also, you may have noticed that, when the upper MOSFET(Q1) turns on, the gate of the lower MOSFET(Q2) gets pulled high. This is caused due to the reverse transfer capacitance of the MOSFET (Cdg).
When Q1 turns on, the node between the two MOSFETs suddenly gets pulled high. Due to this sudden appearance of a voltage at that node (to with the drain of Q2 is connected), the gate of Q2 gets charged through the reverse transfer capacitance of Q2. A lower gate resistor or a diode will help suck this unwanted current into the driver and preventing the gate from being pulled up.
It is important to ensure that both MOSFETs of the halfbridge switch cleanly with a clear deadtime, or else there will definitely be a cross-conduction, which can stress the MOSFETs and cause a dip in the power supply.