The phase behaviour of blends of poly(acrylonitrile:methyl acrylate: butadiene) (B210) and polyolefins modified with polar groups, either by copolymerization or grafting reactions, was examined using differential scanning calorimetry (DSC). Enhanced or complete miscibility was attained by synthetically incorporating molecular features which promote intermolecular attraction. Miscibility over the entire range of compositions was found for binary blends of B210 and poly(ethylene-co-maleic anhydride) (PEMA). For other blends such as B210 and poly(propylene-g-acrylic acid) (PP-g-AcA) or poly(ethylene-g-maleic anhydride) (PE-g-MA), miscibility was limited to the amorphous phase. Several equations commonly used in the literature to express the glass transition temperature-composition relationship have been applied to describe the miscible blend systems. Gordon-Taylor and Kwei equations best represent the T_g data of these polymer mixtures. The deviation from linearity of both experimental and predicted values was attributed to the existence of specific intermolecular interactions between the constituents of the individual polymer chains. This work has shown that it is possible to combine the desirable features of polyolefins (low permeability to moisture) and acrylonitrile-based polymers (good gas barrier properties) by creating a miscible blend through molecular modification.