Monte Carlo simulations with energies computed via the tight-binding model are applied in studying the equilibrium properties of the interface layer in the system Pb/Cu(110). In a submonolayer range below 0.5 ML (ML monolayer), the model based on the coverage-dependent interactions reveals a lattice-gas random adsorption, an equilibrium adatom-substrate intermixing and formation of a centred c(2 × 2) phase. The process of intermixing is found to be coverage and temperature dependent. At high adatom concentration, 0.75-0.80 ML, as a result of very subtle competition between the strain energy and the energy gain due to mixing, the system forms a succession of commensurate unidimensional p(n × 1) structures. The results are in line with those recently obtained from scanning tunnelling microscopy and thermal energy atom scattering observations.