In our studies we present a multilayer structure consisting of outer layers of two-ply basalt composed of basalt fabric impregnated with an epoxy compound and an inner layer of polyurethane reinforced with basalt, having the same composition, formed in conjugate hexagonal prisms, and forming a cellular framework. The main part describes the technological sequence of obtaining basalt face layers, basalt hexagonal cellular frame, and filling it with a liquid reaction mass of rigid polyurethane system. The formation of a single multilayer composite structure is shown. We also present the results of the experimental research of strength of a laminated composite and its inner layer without facing layers when tested for static bending with concentrated load increasing at a constant rate and compression testing up to 10% of relative deformation. It describes the effect of the size of hexagonal prismatic cells of the frame on the physical and mechanical characteristics of the middle layer. The reduction of the cell size results in the increase of the composite strength. The dependence of the composite density on the size of the cells of the basalt frame has been studied.