Lateral GaN-on-Si HEMT technology enables integrated high-voltage half-bridges with gate drivers. However, the capacitive coupling through a common conductive substrate influences switching characteristics. The measured hard-switching turn-on time with floating substrate increased to over 16 ns as compared to conventional source-connected substrate (1 ns), switching 300 V/4A with GaN ICs comprising 600V HEMTs with integrated single-input depletion-load inverter controlled pull-up driver. Simulations of the GaN IC in half-bridges using a four-terminal transistor model (including substrate capacitances) are first verified by some measurements (real prototypes). Then a comprehensive parameter study is carried out using simulations (virtual prototype) for four half-bridge substrate terminations, two integrated driver circuits, and high/low-side and hard/resonant turn-on/off switching. New insights into coupling effects influencing switching losses and switching time are used to develop a robust IC in terms of capacitive substrate coupling.