Combining elasticity theory with electrostatics, we calculate the actuation response of a charged multilayer film, which is composed of consecutively stacked piezoelectric and polymeric elastomer layers, with respect to an applied voltage. Depending on the individual material properties and polarity of the applied voltage, we show that the composite multilayer can exhibit actuation properties which are considerably better than the response of the individual constituents. It is also shown that there is a window for applied voltages within which the thickness of the composite film expands, a condition that cannot be achieved in single layer films. In particular, we apply and evaluate our theory for various piezoelectric and dielectric elastomers. The results obtained will be helpful to develop tailored composite materials with specific actuation characteristics.