Note that lead inductance is included in the models (I assume -- you didn't show the models, so I guess they're going to be the ones from the mfg?), and you're seeing transients due to that.
Note that C1 is redundant, unless you've specified different ESR/L for each, which isn't indicated so I'm going to assume they are pure C. (A poor assumption in LTSpice, which likes to put default parasitics on components for you.)
And yeah, you've got a 100ns dead time, which turns on the body diode, which then undergoes recovery. SPICE is notoriously bad at recovery, but this model seems reasonably okay.
If you can handle tighter timing with the controller/driver you'll be using, consider setting dead time on the rising edge to nearly interference (say -20/0 or even -10/10 ns). Add some series inductance (besides the package inductance) to set commutation dI/dt. (Absorb the inductor's energy in an RC, or use an R||L, or a Vpeak clamp snubber.) Consider adding C (or a lower R and larger C R+C) to set dV/dt at nominal load current to help prevent diode forward bias.
Alternately, use an R || D gate resistor for the low side, to delay turn-off to the same end.
If the load current is bidirectional, ideally you'd have adaptive dead time and/or drive strength (depending on load current magnitude and direction), but the next best is fixed timing with short dead time, or interference, on both edges.
Tim