Poly(ethylene-co-vinyl acetate)/organically modified clay nanocomposites were prepared using different clay loadings and by varying the amount of organic modifier. The morphology of the nanocomposites was investigated using small-angle X-ray scattering (SAXS), scanning electron microscopy (SEM), and transmission electron microscopy (TEM). SAXS results displayed intercalation of polymeric chains between the silicate layers in all the cases. The interlayer distance varies slightly between the series. TEM images showed a better dispersion of the clay platelets at lower loading for both series of samples. The pervaporation performances of membranes were analyzed using a chloroform/acetone mixture. Membranes displayed high selectivity. The influence of feed composition on pervaporation was analyzed. The nanoclay content and the influence of free volume on pervaporation performance were also investigated in detail. A drop in selectivity and an increase in permeation rate were observed at higher clay loadings.