Polymer adhesion between two immiscible polymers is usually poor because there is little interpenetration of one polymer into the other at the interface. Increasing the width of the interfacial zone can enhance adhesion and mechanical properties. In principle, this can be accomplished by exposing heterogeneous polymer materials to a high-pressure fluid. The fluid can act as a common solvent and promote interpenetration. It also increases chain mobility at the interface, which helps to promote "welding" of the two polymers. A combination of the gradient theory of inhomogeneous systems and the Sanchez-Lacombe equation of state was used to investigate this phenomenon, especially the effect of the high compressibility of supercritical (SC) fluid on the compatibilization of two incompatible polymers. We calculate the interfacial density profile, interfacial thickness, and interfacial tension between the two polymers with and without the SC fluid. We find that the interfacial tension is decreased and the interfacial thickness is increased with high-pressure SC fluid for the ternary systems we have investigated. As the critical point is approached and the SC compressibility becomes large, no enhancement or deleterious effects on compatibilization were observed.