Transformation between locomotion modes in multimodal robots poses significant design challenges to meet the growing demand for exploration in various environments. Design constraints involved for an aerial-aquatic robot must account for air and water maneuverability efficiently while minimizing the amount of energy expenditure. Recently, flying fish (Exocoetidae) have gained increasing attention for their ability to switch locomotion modes. Flying fish wings are elastic membranes with no muscles present; instead, fin rays lend support to the flexible structure. A bioinspired deployable wing is presented here based on observations of the flying fish. Specifically, we propose a lightweight and self-stiffening foldable membrane. Self-stiffening is achieved by leveraging spring origami bistability design principles allowing for multistable operations including deployment (~1 s), and collapse for flying, and swimming modes, respectively. Additive manufacturing was utilized to fabricate the wing weighing ~7.5% of the target 500 g multimodal robot. Additionally, structural and aerodynamic experiments designed for gliding speeds of up to 8.5 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\displaystyle \frac{m}{s}$</tex> revealed that the wing remained deployed and avoided undesired collapse. The same wind tunnel experiments revealed a higher lift coefficient, and glide ratio for the proposed wing, compared to a flat wing, and rigid wing, respectively, owing to the multifunctional membrane architecture.