Polyelectrolyte complex membranes (PECMs) were prepared by combining sodium carboxymethyl cellulose (NaCMC) and gelatin (Ge) with variations in the Ge content in the NaCMC matrix. Characterization methods, such as infrared spectroscopy (FTIR), wide-angle X-ray diffraction (WAXD), thermogravimetric analysis (TGA), scanning electron microscopy (SEM), contact angle analysis (CA), and universal testing machines (UTM) were used to investigate the physicochemical studies of the prepared membranes. The pervaporation characteristics of membranes with Ge content were investigated using an azeotropic mixture of water and bioethanol. The obtained data revealed that the membrane with 15 mass% of Ge (M-3) showed a maximum flux of 7.8403 × 10−2 kg/m2·h with separation selectivity of 2917 at 30 °C. In particular, the total and water flux of PECMs are shown as very close to each other indicating that the fabricated membranes could be employed to successfully break the azeotropic point of water–bioethanol mixtures. Using temperature-dependent permeation and diffusion data, the Arrhenius activation parameters were calculated, and the obtained values of water permeation (Epw) were considerably smaller than bioethanol permeation (EpE). Developed membranes showed the positive heat of sorption (ΔHs), suggesting that Henry’s sorption mode is predominant.