A theoretical approach is presented to relate the equilibrium surface pressure (ESP) of binary mixtures of water-insoluble surfactants to the equilibrium surface pressures of the pure components. The approach is based on the application of a two-dimensional (2D) solid-on-solid model for an exact computation of the surface pressure. The Hamiltonians describing the energetic cost for the creation of "mixed" interfaces are constructed considering configurations with one random walk. The performed numerical computations use a single parameter for an evaluation of the interfacial intermolecular interactions between like and unlike molecules. The predictions of the 2D solid-on-solid model in the case of non-ideal mixing are compared with experimental results for ESP of two-component phospholipid-alkanoic acid surfactant mixtures.