The Flory-Huggins equation was used to describe results of total and preferential sorption measurements for the binary liquid mixture of benzene (1) and alcohol (2) in one of two nonporous polymer membranes (3), low-density polyethylene (LDPE) and Nafion membrane. The concentration dependence of binary and ternary interaction parameters was determined. The interaction parameters for the benzene - methanol binary mixture were obtained from binary vapor-liquid equilibrium data in the literature to decrease the number of adjusted parameters. The results show that use of a ternary interaction parameter is necessary. Data treatment was performed assuming either no crystallinity or an average crystallinity typical for the studied membranes. Subsequently, the limiting activity coefficients of solutes in LDPE were calculated from the values of the interaction parameters and their values compared to values of the limiting activity coefficients of benzene and methanol in hypothetical liquid alkane with the same density as LDPE obtained by the UNIFAC method. POLYM. ENG. SCI., 55:1187-1195, 2015. (c) 2014 Society of Plastics Engineers