Electrically insulating polymer dielectrics with high energy densities and excellent thermal conductivities are showing tremendous potential for dielectric energy storage. However, the practical application of polymer dielectrics often requires mutually exclusive multifunctional properties such as high dielectric constants, high breakdown strengths, and high thermal conductivities. The rational assembly of 2D nanofillers of boron nitride nanosheets (BNNS) and reduced graphene oxide (rGO) into a wellaligned micro-sandwich structure in polyimide (PI) composites is reported. The alternating stacking of rGO and BNNS synergistically exploits the large difference in their electrical conductivities to yield a high dielectric constant with a moderate breakdown strength. Moreover, the distinctively separated rGO and BNNS layers give rise to higher thermal conductivities of composites than those containing mixed fillers because of reduced phonon scattering at the interfaces between two identical fillers, as verified by molecular dynamics simulations. Consequently, the micro-sandwich nanocomposite prevails over the PI film with a simultaneously high dielectric constant of ≈579, a high energy density (43-fold higher than PI) and an excellent thermal conductivity (11-fold higher than PI) at a low hybrid filler content of only 2.5 vol%. The multifunctional nanocomposites developed in this work are promising for flexible dielectrics with excellent heat dissipation.