Understanding the physical processes involved in interfacial heat transfer is critical for the interpretation of thermometric measurements and the optimization of heat dissipation in nanoelectronic devices that are based on transition metal dichalcogenide (TMD) semiconductors. We model the phononic and electronic contributions to the thermal boundary conductance (TBC) variability for the MoS2-SiO2 and WS2-SiO2 interface. A phenomenological theory to model diffuse phonon transport at disordered interfaces is introduced and yields G = 13.5 and 12.4 MW K-1 m-2 at 300 K for the MoS2-SiO2 and WS2-SiO2 interface, respectively. We compare its predictions to those of the coherent phonon model and find that the former fits the MoS2-SiO2 data from experiments and simulations significantly better. Our analysis suggests that heat dissipation at the TMD-SiO2 interface is dominated by phonons scattered diffusely by the rough interface although the electronic TBC contribution can be significant even at low electron densities (n ≤ 1012 cm-2) and may explain some of the variation in the experimental TBC data from the literature. The physical insights from our study can be useful for the development of thermally aware designs in TMD-based nanoelectronics.