Poly(vinyl alcohol) (PVA) membranes crosslinked with poly(acrylic acid-co-maleic acid) (PAM) were prepared to investigate the effect of aging on their morphology by swelling them for up to 7 days. PAM was used both as a crosslinking agent and as a donor of the hydrophilic-COOH group. A $30 wt\%$ weight loss of the dry membrane was observed in the swelling test after 6 days. The surface of the membrane was dramatically changed after the swelling test. The surface roughness of the PVA/PAM membrane was increased, as determined by atomic force microscopy (AFM). The swelling loosened the polymer structure, due to the release of the unreacted polymer and the decomposition of the ester bond, thereby resulting in an increase in the free volume capable of containing water molecules. The water molecules present in the form of free water were determined by differential scanning calorimetry (DSC). The fraction of free water increased with increasing swelling time. The swelling of the membrane may provide space for the transport of protons and increase the mobility of the protonic charge carriers. The proton conductivity of the membranes measured at T= 30 and $50^{circ}C$ was in the range of $10^{-3} to 10^{-2} S/cm$, and slightly increased with increasing swelling time and temperature.