Lightweight, strong, and energy-absorbing materials are highly sought after in practical engineering applications. To this end, interpenetrating phase composites (IPC) stand as a novel class of composite materials to better leverage the properties of their constituents. Their structural design, however, has been limited to only specific structural features at a certain length scale in the existing studies. Inspired by the hierarchical composite materials in nature, this work proposes a novel concept of hierarchical interpenetrating phase composites (HIPC) by polymer infiltration into 3D printed hierarchical porous ceramic lattices. The hierarchical porous alumina lattices have up to three levels of porosity, including 3D printed macropores (≈300 μm), emulsion-templated micropores (≈10 μm), and sub-micropores (<1 μm) from partial sintering. Upon epoxy infiltration, three-level HIPC is constructed with hierarchically incorporated epoxy domains and alumina-epoxy interfaces, which leads to its unique multi-scale mechanical energy absorption mechanisms. Featuring a particularly porous and lightweight ceramic lattice, three-level HIPC exhibits an excellent combination of high specific compressive strength (64.6 kN m/kg), specific flexural strength (39.2 kN m/kg), and SEA (18.4 kJ/kg). In addition, even with a low ceramic content, three-level HIPC can effectively enhance the thermal conductivity via its hierarchically continuous ceramic microstructure. Therefore, our three-level HIPC has demonstrated impressive mechanical and thermal enhancement with its exquisite hierarchical architecture. The hierarchical structural engineering approach also represents a paradigm shift from constructing single-scale IPCs to multi-scale HIPCs and can be extended to other material combinations for high-performance structural and functional materials.