Multicomponent epoxy micro/nano-composites containing micro-alumina, micro-quartz, and nano-silica were fabricated to develop electrical insulation materials with high thermal conductivity. Simply changing the ratio between the alumina and quartz microparticles caused a trade-off relationship between the thermal conductivity and electrical insulation. Increasing the alumina content in the epoxy-alumina/quartz micro-composites enhanced the thermal conductivity but deteriorated the dielectric strength. An increase in the thermal conductivity without incurring a loss in the dielectric strength was achieved by incorporating silica nanoparticles in the epoxy micro-composites. Adding silica nanoparticles to the epoxy micro-composites was found to be more efficient in improving the thermal conductivity compared to increasing the alumina ratio, especially at low alumina/quartz ratios. This behavior corresponded to theoretical models. Therefore, we provide a useful insight, both practical and theoretical, into the more advanced optimization of designing multicomponent epoxy composites for electrical insulation with high thermal conductivity.