Alloy effective pair interactions (EPIs) are crucial quantities to characterize the bulk and surface thermodynamical properties of alloys. In this paper we focus on the influence of a size mismatch between the components of an alloy, by considering the illustrative example of the Cu–Ag system. Using N-body interatomic potentials derived from the second-moment approximation of the tight-binding scheme, we compute the EPIs in the bulk and in the (0 0 1) surface for the two infinitely dilute limits. Both the bulk and the surface EPIs obey a two-domain rule. The first two EPIs hold a specific behaviour that depends linearly on the value of the mixed interaction, while the others originate in elasticity and hold a behaviour that can be made general by an appropriate normalization. We observe that a dilatation as well as a contraction of the lattice parameter can reverse the sign of the first two bulk EPIs. Moreover, the observed sign reversal between the bulk and the surface first EPI is due to an additive factor (and not a multiplicative one) induced by the size mismatch. The elasticity-related surface EPIs hold a very anisotropic behaviour, as significant values are restricted to the close-packed directions of the (0 0 1) surface. These values decay exponentially with the distance along these directions, in a direct relation with the exponential decay of the surface relaxations. These EPIs have also been computed for the non-equivalent sites of the c(10 × 2) superstructure of an Ag-pure plane on a Cu(0 0 1) substrate. They reveal a very large heterogeneity between the sites which accompanies the one due to the permutation enthalpy, the second energetic quantity involved in the determination of the 2D phase diagram.