Abstract This work numerically explores the anisotropy, impact phase wave propagation, buckling resistance, and natural vibration of ultra-high performance concrete (UHPC) and UHPC-steel interpenetrating phase composite (IPC) with triply periodic minimal surfaces (TPMSs), including sheet and solid gyroid, primitive, diamond, and the Schoen I-graph-wrapped package (I-WP). The experiment is conducted to verify the accuracy of the numerical model in terms of Young's modulus of polylactic acid (PLA)-based TPMS lattices and PLA-cement IPCs with TPMS cores, with the highest percent difference of 15% found for IPCs and 17% found for lattice. The results indicate that UHPC material with sheet gyroid exhibits the least extreme anisotropy in response to the varying orientation among other lattices regardless of the change of solid density, making it the ideal candidate for construction materials. Interestingly, compared to UHPC-based TPMS lattice, IPCs possess a much smaller anisotropy and exhibit almost isotropy regardless the variation of solid density and TPMS topology, offering a free selection of TPMS type to fabricate IPCs without much care of anisotropy. The phase wave velocity and buckling resistance of UHPC- and IPC-based beams with TPMSs nonlinearly decrease with a drop of TPMS solid density, but it is the almost linear pattern for the case of natural vibration frequency. UHPC material and IPC with sheet gyroid lattice are found to possess the lowest phase wave velocity and exhibit the least anisotropy of wave propagation, showing it as an ideal candidate for UHPC material to suppress the destructive energy induced by the external impact.