We present a model for the electrostatic response of the copper-water interface, which takes into account the electronic, Stern layer, and double layer contributions. The electronic and Stern layer contributions are not separated, but are modeled together using a direct dynamics model of the copper-water interface which we introduced earlier. The boundary condition for the double layer contribution is chosen to be consistent with electric fields calculated explicitly from the molecular dynamics simulation. We find results which are consistent with some experimental results for the capacitance of the low-index surfaces of copper. A remarkable feature of the results is that the calculated macroscopic electric field is much more effectively screened near the interface than it is in classical molecular dynamics models.