We present an improved method to model the small-signal behaviour of GaN-based metal insulator semiconductor high electron mobility transistor (MIS-HEMT) gate stacks biased in the 'spill-over' regime, where electrons accumulate at the 'critical' dielectric/III-N interface. In this regime, the small-signal admittance can capture the response of traps at the critical interface up to 1 eV below the conduction band-edge (EC) at elevated temperatures. This allows accurate extraction of the interface trap density (Dit) which parameterizes the MIS gate stack quality, that in turn strongly influences device functionality and reliability. However, accurate extraction of Dit from the small-signal characteristics requires that admittance contributions from interface traps and the intrinsic (i.e. trap-free) gate stack are carefully separated. The lumped element model (LEM) proposed here does this effectively and achieves a better match to experimental measurements than previously reported. © 2020 IEEE.