Continuous and robust filler network is very critical in improving thermal conductivity of the thermally conductive yet electrically insulating composite. Regrettably, such network is commonly constructed by large amount of thermally conductive while electrically insulating fillers with sacrificing mechanical properties of the final composite. In the present work, to address this issue and further improve the thermally conductive property, the robust 3D thermally conductive while electrically insulating hybrid filler network with high orientation and ordered distribution was constructed successfully through strong shear and extension flow field in confined space during the multilayer co-extrusion. In the hybrid filler network with the 32-layer alternating structure, along the extrusion direction, graphite (Gt) flakes were highly oriented; meanwhile, along the thickness direction, the local Gt-MWCNTs network was confined between two adjacent SiC-filled layers. As a result, thermal conductivity of the final composite reached as high as 2.05 W/(mxK). Furthermore, significantly anisotropic electrical resistivities were also obtained, which endowed the final composite with excellent electrical insulation, great anti-static and electromagnetic interference shielding properties. Moreover, compared with commonly compounded composites, mechanical properties of the multilayered composite were also enhanced significantly. As a consequence, the multifunctional composite with robust thermally conductive while electrically insulating filler network and excellent mechanical properties can be obtained based on this strategy, thus it plays a critical role in facilitating the development of the thermal management materials.