The idea of extending functions of graphene aerogels and achieving specific applications has aroused wide attention recently. A solution to this challenge is the formation of a hybrid structure where the graphene aerogels are decorated with other functional nanostructures. An infiltration-evaporation-curing strategy has been proposed by the formation of hybrid structure containing poly(dimethylsiloxane) (PDMS) and compressible graphene aerogel (CGA), where the cellular walls of the CGA are coated uniformly with an integrated polymer layer. The resulting composite shows enhanced compressive strength and a stable Young's modulus that are superior to those of pure CGAs. This unique structure combines the advantages of both components, giving rise to an excellent electromechanical performance, where the bulk resistance repeatedly shows a synchronous and linear response to variation of the volume during compression at a wide range of compressed rates. Furthermore, the foamlike structure delivers a water droplet with "sticky" superhydrophobicity and a size as large as 32 μL that remains tightly pinned to the composite, even when it is turned upside-down. This is the first demonstration of superhydrophobicity with strong adhesion on a foamlike structure. These outstanding properties qualify the PDMS/CGA composites developed here as promising candidates for a wide range of applications such as in sensors, actuators, and materials used for biochemical separation and tissue engineering.