A method of forming a three-dimensional (3D) composite structure includes: securing a mask between a collimated light source and a volume of a photo-monomer; directing a collimated light beam from the collimated light source to the mask for a period of exposure time such that a portion of the collimated light beam passes through the mask and is guided by a plurality of apertures into the photo-monomer to form a plurality of waveguides through a portion of the volume of the photo-monomer; removing any uncured photo-monomer to leave behind a three-dimensional ordered open-cellular microstructure to define an open volume and a structure of a first continuous material of the three-dimensional composite material; and placing a second continuous material in the open volume, wherein the second continuous material and the first continuous material share an interface between each other, and wherein the interface is everywhere continuous.