Electronic materials that allow the controlled flow of electrons in aqueous media are required for emerging applications that require biocompatibility, safety, and/or sustainability. Here, a composite hydrogel film composed of graphene and catechol is electrofabricated, and that this composite offers synergistic properties is reported. Graphene confers metal-like conductivity and enables charge-storage through an electrical double layer mechanism. Catechol confers redox-activity and enables charge-storage through a redox mechanism. Importantly, there are two functional populations of catechols: conducting-catechols (presumably in intimate contact with graphene) allow direct electron-transfer; and non-conducting-catechols (presumably physically separated from graphene) require diffusible mediators to enable electron-transfer. Using a variety of spectroelectrochemical measurements, that the capacity of the composite for charge-storage increases in proportion to the extent by which the catechol-groups can undergo redox-state switching is demonstrated. To illustrate the broad relevance of this work, how the redox-state switching can be related to both the charge storage of energy materials and the memory of molecular electronic materials is discussed. The authors believe this work is significant because it demonstrates that: conducting and redox-active components enable distinctly different mechanisms for charge-storage and electron-transfer; these components act synergistically; and mediators provide unique opportunities to extend the capabilities of electronic materials.