A thermodynamic model of multicomponent fluid membranes under the influence of lateral forces is described. Membrane components are characterized by their effective molecular areas, molecular charges, and the set of critical demixing coefficients (differential interaction energies) between each of the different species present. This model is useful in the analysis of electric field induced concentration gradients in supported lipid bilayer membranes; It has been employed to determine the critical temperature for spontaneous lateral phase separation of a mixture of cardiolipin and phosphatidylcholine from field-induced concentration profiles of a fluorescent probe. More generally, it provides a convenient way of interpreting critical demixing effects in multicomponent membranes and exploring the way these influence the response of a membrane to lateral forces.