In this work a general approach is proposed for modelling of multicomponent multiphase film-like systems. It integrates into a single whole the Maxwell-Stefan formulation of multicomponent diffusion and partial differential equations of continuum mechanics. The former enables multicomponent diffusional interactions (cross-effects) to be taken into account, the latter makes it possible to avoid design trouble caused by the employment of mass-transfer and heat-transfer coefficients. The proposed approach is applicable to a variety of multicomponent separation processes where phase boundaries and interfaces can be properly determined. In the present work attention is focused on the application to the processes with the film-like hydrodynamics and geometry. These include both film flows and more complicated structures allowing hydrodynamic analogy between simple and complex flow to be established, in particular, porous media and structured packing flows. The application is illustrated with an example of multicomponent liquid film pertraction - a three-phase membrane extraction in falling liquid films.