The effect of the concurrent action of intermolecular and molecule substrate interactions on the two-dimensional (2D) self-assembly of organic molecules on solid surfaces is investigated in a combined experimental and theoretical effort. Scanning tunneling microscopy measurements of terephthalic acid on the Cu(111) surface, a model system where the interplay between the two interactions is particularly evident, are used to develop a general, simple, and computationally inexpensive model that quantitatively accounts for the experimental observations. The model, related to the well-known Frenkel-Kontorova model, offers a comprehensive description of the "subtle interplay" between intermolecular and molecule-substrate interactions and provides a qualitative and quantitative predictive capability in the design and fabrication of 2D molecular nanostructures at surfaces.