This paper is an effort to solve the issue related to the electrically insulating polymer composites for thermal interface materials applications. A novel strategy is designed to achieve both enhanced thermal conductivity and high electrical insulation of epoxy composites by combining one-dimensional boron nitride nanotubes (BNNTs) and two-dimensional boron nitride nanosheets (BNNSs). A noncovalent functionalization approach is used to functionalize and solubilize hybrid BNNTs/BNNSs fillers by 1-pyrenebutyric acid (PBA) molecules. The PBA-functionalized BNNTs/BNNSs exhibit good dispersion and high compatibility with epoxy matrix. The epoxy composites with PBA-functionalized BNNTs/BNNSs hybrid fillers yield a thermal conductivity of 0.47 W m−1 K−1 and an electrical resistivity of 9.3 × 1016 Ω cm at 2 wt% filler loading, which outperform the epoxy composites with individual PBA-functionalized BNNTs or BNNSs fillers.