With the ever-increasing requirements placed on current and future pulsed power systems in terms of voltage, power, and compactness; solid insulation is a strong candidate for the development of novel insulation systems capable of meeting these specifications. However, the issue of solid-solid interfaces under non-standard and fast-rising impulses must firstly be addressed, as the failure to do so may pose significant risk of electrical breakdown due to reduced dielectric strength across interfacial contacts. In this work, the impulsive breakdown characteristics across dry-mate solid interfaces formed between PVC (polyvinylchloride), Torlon (polyamide-imide), Delrin (polyoxymethylene), Perspex (polymethylmethacrylate), and Ultem (polyetherimide) has been investigated in atmospheric air and under two different impulsive waveforms rising at ∼2400 kV/µs and ∼0.35 kV/µs. The statistical treatment of the obtained impulsive breakdown voltages and time to breakdowns are presented, alongside an analysis of the post-breakdown surfaces and discharge channel morphologies. The results indicate that under low mating pressure conditions (10’s of kPa), the interfacial breakdown strength may be below that of only an air gap with no dielectrics. A correlation between the estimated asperity aspect ratio and the interfacial breakdown strength has been observed. This suggests that under the present experimental conditions, field enhancement around surface asperities may be a dominating factor which defines the breakdown strength of the interface, since the surface asperities do not deform sufficiently to form strong interfacial contact spots, and thus reducing the interfacial tracking resistance. This therefore provides little to impede the development of interfacial discharges. The widths of post-breakdown traces left by plasma channels on the contacting surfaces have also been shown to be dependent on the rate of voltage rise, dV/dt, and on the material forming the interface. The results arising from this work may aid in the future development of high voltage solid insulating systems for power and pulsed power systems.