A composite material comprises a polymer matrix having microstructure filler materials that comprise a plurality of interconnected units wherein the units are formed of connected tubes. The tubes may be formed by photo-initiating the polymerization of a monomer in a pattern of interconnected units to form a polymer microlattice, removing unpolymerized monomer, coating the polymer microlattice with a metal, removing the polymer microlattice to leave a metal microlattice, growing or depositing a material on the metal microlattice such as graphene, hexagonal boron nitride or other ceramic, and subsequently removing the metal microlattice.