The statistical thermodynamics of binary mixtures with non-additive lateral interactions was developed on a generalization in the spirit of the lattice-gas model and the classical quasi-chemical approximation (QCA). The traditional assumption of a strictly pairwise additive nearest-neighbors interaction is replaced by a more general one, namely that the bond linking a certain atom with any of its neighbors depends considerably on how many of them are actually present (or absent) on the sites in the first coordination shell of the atom. The total and partial adsorption isotherms are given for both attractive and repulsive lateral interactions between the adsorbed species. Interesting behaviors are observed and discussed in terms of the low-temperature phases formed in the system. Comparisons with Monte Carlo simulations are performed in order to test the validity of the theoretical model. (C) 2016 Elsevier B.V. All rights reserved.