A structural panel includes a shell having spaced first and second exterior panels and frame members adjacent edges of the panels, and at least one polymeric sheet disposed between the exterior panels and bonded to an adjacent exterior panel. The polymeric sheet is made of a thermoplastic material and has a plurality of openings through its thickness spaced apart by flat wall portions of the polymeric sheet. Stiffeners are disposed between the polymeric sheets and are secured by polymeric end caps. The end caps are made of a thermoplastic material and have a plurality of openings through their thickness for receiving the stiffeners. A foam insulation material fills substantially all the space between the polymeric sheets, stiffeners, and frame members in the shell interior. At least one blast- or ballistic-resistant core layer may be disposed adjacent the at least one polymeric sheet.