Interlocking laminated structural roofing panels have a lightweight foamed core sandwiched between outer and inner layers of materials such as wood, polymer materials, fire resistant and/or waterproof membranes, and metal layers. At least one layer is a self-gripping metal sheet that grips and bonds mechanically to adjacent layers such as wood layers. A self-gripping metal sheet may be used on both sides of the roofing panels to form a panel that is strong, structurally robust, and able to span between relatively widely spaced roof rafters with little or no mid-span support. Interlocking features along the edges of the panels interlock adjacent panels together to form a strong monolithic roof covering for a roof.