We investigate film morphologies of heteroepitaxial face-centered cubic (fcc) thin metal adlayers grown on fcc(111) metal substrates using a statistical-mechanical mean-field theory. In order to develop a general understanding of how various intrinsic properties of the film and substrate dictate the thermodynamically-preferred film structures, fourteen fcc(111)/fcc(111) interfaces with lattice mismatches ranging from -17% to +21% and bulk cohesive energies ranging from 2 to 6 eV/atom are examined. We find that relative magnitudes of lattice mismatch, surface energy, and bulk cohesive energy all contribute to determining the film structures, in contrast to our findings for fcc(100) interfaces, where lattice mismatch played the dominant role. Pseudomorphic growth is predicted to be preferred for small-mismatched interfaces, while incommensurate films are favored for large-mismatched interfaces. When the film has a lower surface energy and bulk cohesive energy than the substrate, layer-by-layer or Stranski-Krastanov growth is favored. Three-dimensional growth becomes dominant for interfaces where the relative surface and bulk cohesive energy of the film is large compared to the substrate. We also find the film structures are insensitive to temperature variations in the range 300-800 K. Finally, our theoretical calculations are in generally excellent agreement with experimentally-determined film structures, and we have gone further to predict the morphological nature of a number of heterointerfaces that have yet to be examined experimentally.