We present the results of an investigation of Rh films on Ag(100). The films are studied using Auger-electron spectroscopy, low-energy electron diffraction, x-ray photoelectron spectroscopy, ultraviolet photoemission spectroscopy, ion-scattering spectroscopy, and scanning Auger microscopy. Overlayer characteristics are examined at substrate temperatures of 300 and 600 K. We find that the equilibrium configuration is not predicted by any of the three traditional growth modes (Frank–Van der Merwe, Stranski-Krastanov, or Volmer-Weber). Rather, the equilibrium film structure is that of a Ag-Rh-Ag sandwich, most probably flat. Formation of the sandwich is thermodynamically driven by the difference in surface free energies between Ag and Rh, and is kinetically accessible because of the high mobility of the Ag atoms.