Extendable structures often use rollable designs, with long, flexible materials that can be wound onto a hub for storage without the need for joints. However, achieving high stiffness and strength in the extended state while keeping the hub compact is challenging, given that stiff structures are difficult to bend and typically require larger hubs for storage. Here, we introduce a corrugated sheet-shaped foldable design that enables Z-folding by connecting multiple strips in parallel. The unfolded, corrugated form structure offers a high load-bearing capacity, and the folded, stacked form structure can be smoothly rolled onto a hub, enabling fold-and-roll storage. The key innovation is the formation of an interlaced origami structure by connecting strips through a ribbon-weaving technique. This interlacing design enables both localized flexibility and mutual constraints between strips: The localized flexibility accommodates perimeter differences between stacked strips during rolling, and the densely repeated mutual constraints make the corrugation resist excessive deformation under external forces. Using these structures, we made two deployable mobile robots: one with a 1.6-meter deployable arm for shelving tasks and another with a tetrahedral deployable frame that supported a meter-scale 3D-printing system. Our results showcase the potential of this interlaced, corrugated approach for deployable robotic systems requiring both compactness and strength.