The contact area between solid insulations, namely solid-solid interfaces, affect the dielectric characteristics of an entire insulation system. With the theoretical and experimental studies covered in this paper, we intend to investigate the effects of the elastic modulus, interface contact pressure, and surface smoothness/roughness on the tangential AC breakdown strength (BDS) of contact surfaces at dielectric interfaces that undergo tangential electric stress. Four distinct solid dielectric specimens with various elastic modulus values were employed. The interfaces between the same materials were subjected to AC breakdown and partial discharge (PD) detection tests at different contact pressure values. In addition, the interface surfaces were polished using four different sandpapers of various grits to scrutinize the effect of surface roughness. A deterministic model built around the contact mechanics of solid surfaces was proposed to determine the sizes of the interfacial cavities and to simulate the 3D displacement of the surface protrusions based on the surface roughness, contact pressure, elastic modulus, and hardness of an interface. The estimated sizes of cavities and contact areas were then coupled with a comprehensive breakdown model that addressed cavity discharge and breakdown of contact areas, separately. The results by the model were correlated with the results of the AC breakdown and PD experiments to elucidate not only how cavities were linked at solid-solid interfaces but also the effects of roughness, elasticity, contact pressure, and gas pressure inside cavities.