3D Graphene sponge (GS) supported boron nitride (BN) skeleton (BN@GS) was fabricated through a facile method by using ammonium sulfide under mild conditions. Then, BN@GS sponge was infiltrated by epoxy resin to prepare the composites. The microstructures of BN@GS were controlled by adjusting the mass ratio of GS to BN and the dimension of BN to obtain thermally conductive but electrically insulating polymer composites. The thermal and electrical properties of composites were investigated and the results showed that thermal conductivity of composites reached 0.588 W m−1 K−1 at a low GS loading of 0.157 wt%, which was twice as large as the BN/epoxy composites without graphene. When the mass ratio of BN to GS was 60:1 and 100:1, the electrical conductivity of the resin composites corresponded to insulator region. The 3D continuous network of GS endowed the composites with enhanced thermal conductivity at a relatively low filler loading. In addition, the introduction of BN cut off the transmission of electrons which resulted in the composites with electrical insulation. The hybrid fillers were introduced to guarantee the enhanced thermal conductivity and electrical insulation at a relatively low filler loading. The thermal conductivity of the BN@GS/epoxy composites coincide well with the surface temperature variation of the BN@GS/epoxy composites acquired from an infrared camera. The mechanical properties of BN@GS/epoxy composites improved remarkably in comparison with pure epoxy resin. POLYM. COMPOS., 40:E1600–E1611, 2019. © 2019 Society of Plastics Engineers