The development of synthetic structures that mimic mechanical actuation in living matter such as autonomous translation and shape changes remains a grand challenge for materials science. In living systems the integration of supramolecular structures and covalent polymers contributes to the responsive behaviour of membranes, muscles and tendons, among others. Here we describe hybrid light-responsive soft materials composed of peptide amphiphile supramolecular polymers chemically bonded to spiropyran-based networks that expel water in response to visible light. The supramolecular polymers form a reversibly deformable and water-draining skeleton that mechanically reinforces the hybrid and can also be aligned by printing methods. The noncovalent skeleton embedded in the network thus enables faster bending and flattening actuation of objects, as well as longer steps during the light-driven crawling motion of macroscopic films. Our work suggests that hybrid bonding polymers, which integrate supramolecular assemblies and covalent networks, offer strategies for the bottom-up design of soft matter that mimics living organisms.