The controllability of the microstructure of a compressed hierarchical building block is essential for optimizing a variety of performance parameters, such as thermal management. However, owing to the strong orientation effect during compression molding, optimizing the alignment of materials perpendicular to the direction of pressure is challenging. Herein, to illustrate the effect of the ordered microstructure on heat dissipation, thermally conductive carbon‐based materials are fabricated by tailoring dense, orientation–tunable, and interleaved structures. Vertically aligned carbon nanotube arrays (VACNTs) interconnected with graphene films (GF) are prepared as a 3D core‐ordered material to fabricate compressed building blocks of O–VA–GF and S–VA–GF. Leveraging the densified interleaved structure offered by VACNTs, the hierarchical O–VA–GF achieves excellent through‐plane (41.7 W m−1 K−1) and in‐plane (397.9 W m−1 K−1) thermal conductivities, outperforming similar composites of S–VA–GF (through‐plane: 10.3 W m−1 K−1 and in‐plane: 240.9 W m−1 K−1) with horizontally collapsed carbon nanotubes. As heat dissipation plates, these orderly assembled composites yield a 144% and 44% enhancement in the cooling coefficient compared with conventional Si3N4 for cooling high‐power light‐emitting diode chips.