Epoxy resin composites filled with ceramic particles are commonly applied in electrification devices as an electrical insulation. In order to maintain proper functionality of such apparatuses it is crucial to optimize a broad range of properties, such as thermal, mechanical and dielectric parameters. In an earlier paper, a novel core-shell filler was developed in order to enhance the thermal conductivity in the epoxy composite used as electrical insulation. The new filler was made of a standard material, which was covered by a thin layer of high thermally conductive shell, namely, alumina coated by aluminum nitride. It was previously shown that the epoxy resin filled with the core-shell Al2O3@AlN particles showed a significant increase in thermal conductivity with a 63% relative increase. In this paper, a set of complementary measurements was performed and analyzed, namely, rheology, tensile strength, dynamic mechanical analysis, and dilatometry. Moreover, the dielectric permittivity and strength, and electrical resistivity were investigated in order to check if the electrical insulation properties were maintained. The obtained results were compared with the epoxy composite filled with the standard filler. The rheological behavior of the core-shell filled system showed that the processability will not be hindered. The mechanical properties of the composite based on core-shell filler are better than those of the reference system. The coefficient of linear thermal expansion is lower for epoxy filled with core-shell filler, which can lead to better adhesion to internal parts in the electrification devices. The dielectric strength was enhanced by 16% for the core-shell filled epoxy. The investigation clearly demonstrates that the epoxy composite filled with the core-shell particles is an appropriate material for application as electrical insulation with enhanced thermal conductivity.