We report on the mechanical behavior of an interpenetrating carbon/epoxy periodic submicrometer-scale bicontinuous composite material fabricated following the design principles deduced from biological composites. Using microscopic uniaxial compressive tests, the specific energy absorption is quantitatively evaluated and compared with the epoxy/air and carbon/air precursors. The carbon/epoxy material demonstrates extremely high specific energy absorption up to 720 kJ/kg and shear-dominant interphase interactions from the interlocked hard (carbon) and soft (epoxy) phases. Such bicontinuous nanocomposites are a new type of structural metamaterial with designed cell topology and mechanical anisotropy. Their inherent small length scale can play a critical role in prohibiting segregated mechanical responses leading to flaw tolerance.