The thermal conductivity of graphene is limited in the transverse direction due to the exfoliation of the interplanar distance. In this study, the multiwalled carbon nanotubes (MWCNTs) with high thermal conductivities were immobilized into the exfoliated few layers graphene with an objective to enhance the transverse thermal conductivity of MWCNT embedded graphene three-dimensional architectures. Reconstructing the topographically controlled synthetic hybrid nanostructure assemblies in a polymer matrix provides the opportunity to gain insight into the electrical and thermal conduction mechanism. The thickness of the resin layer between the nanohybrid fillers was found to be critical for the phonon transport through the coating whereas this epoxy insulating layer prevents tunneling of the electron. By controlled functionalization and site specific orientations of hybrid nanoscale morphologies in the fiber reinforced composite, the higher mechanical strength could be achieved with increased electrical but reduced thermal boundary resistance of the matrix.