In this paper, we analyze the chemoelectrical behavior of ionic polymer metal composites (IPMCs) in the small voltage range with a novel hypothesis on the charge dynamics in proximity of the electrodes. Specifically, this paper introduces a so-called composite layer which extends between the polymer membrane and the metal electrode. This homogeneous layer describes the charge distribution at the electrode via two species of charge carriers, that is, electrons and mobile counterions. Charge dynamics is described by adapting the multi-physics formulation based on the Poisson-Nernst-Planck (PNP) equations through the incorporation of the electron transport in the composite layer. Under the hypothesis of small voltage input, we use the linearized PNP model to derive an equivalent IPMC impedance model with lumped elements. The equivalent model is represented as a resistor connected in series with the parallel of a capacitor and a Warburg impedance element. These elements idealize the phenomena of charge build up in the double layer region and the faradaic impedance related to mass transfer, respectively. We validate the equivalent model through measurements on in-house fabricated samples addressing both IPMC step response and impedance.