The Maxwell-Stefan (M-S) "frictional" formulation has been used to develop a unified description of mixture permeation across membranes consisting of thin layers of zeolites, metal-organic frameworks or polymers. Explicit analytic expressions are derived for determining the fluxes for steady-state permeation of binary mixtures of species 1 and 2 across a membrane (m), clearly delineating the relative influences of the 1-m, 2-m and interspecies (1-2) frictional contributions. Simplified expressions are derived for two limiting scenarios: negligible 1-2 friction and dominant 1-2 friction; these scenarios help to determine the upper and lower bounds of permeation fluxes and selectivities. The developed model is used to analyze a wide variety of published experimental data on mixture permeation across zeolite and polymer membranes. In each case, the influence of 1-2 friction is analyzed. In cases such as pervaporation across polymer membranes, the 1-2 frictional contribution is found to be extremely significant.