Due to their exceptional mechanical and optical properties, dielectric silicon nitride (SiN) micromembranes have become the centerpiece of many optomechanical experiments. Efficient capacitive coupling of the membrane to an electrical system would facilitate exciting hybrid optoelectromechanical devices. However, capacitive coupling of such SiN membranes is rather weak. Here we add a single layer of graphene on SiN micromembranes (SiN-G) and compare the electromechanical coupling and mechanical properties to bare SiN membranes and to membranes coated with an aluminium layer (SiN-Al). The electrostatic force to external coplanar electrodes of SiN-G membranes is found to be equal to that of the SiN-Al membranes and corresponds to the theoretical value calculated for a perfectly conductive membrane coating. Our results show that a single layer of graphene substantially enhances the electromechanical capacitive coupling of a SiN membrane without significantly adding mass, decreasing the mechanical quality factor or affecting the optical properties.