Polymer composites, with both high thermal conductivity and high electrical insulation strength, are desirable for power equipment and electronic devices, to sustain increasingly high power density and heat flux. However, conventional methods to synthesize polymer composites with high thermal conductivity often degrade their insulation strength, or cause a significant increase in dielectric properties. In this work, we demonstrate epoxy nanocomposites embedded with silver nanoparticles (AgNPs), and modified boron nitride nanosheets (BNNSs), which have high thermal conductivity, high insulation strength, low permittivity, and low dielectric loss. Compared with neat epoxy, the composite with 25 vol% of binary nanofillers has a significant enhancement (~10x) in thermal conductivity, which is twice of that filled with BNNSs only (~5x), owing to the continuous heat transfer path among BNNSs enabled by AgNPs. An increase in the breakdown voltage is observed, which is attributed to BNNSs-restricted formation of AgNPs conducting channels that result in a lengthening of the breakdown path. Moreover, the effects of nanofillers on dielectric properties, and thermal simulated current of nanocomposites, are discussed.