We employed a regular solution-type model to describe the equilibrium segregation of solute atoms on the external surface and at the film-substrate interface in the ultrathin single-crystalline films of binary metal alloys attached to an inert substrate. The finite size of the system, the interlayer interactions in the film and the heteroepitaxial strain in the film were taken into account. We demonstrated that the homogeneous heteroeptiaxial strain in the film affects the surface and interface segregation of solute atoms only in the case when the value of coherency strain parameter (describing the relative change of alloy lattice parameter upon addition of solutes) in the surface and interface layers is different from its value in the rest of the films. The developed model was applied to the Ni(Au) thin films deposited on sapphire substrate. The quantitative agreement between the model predictions and recent experimental data on interface segregation of Au could be achieved by assuming that the film is heteroepitaxially compressed.