The growth and structure of ultrathin Rh films on Fe(100) are studied by grazing scattering of 50 keV He projectiles, incident along "random" and low index surface lattice directions. Oscillations in the specular intensity for scattered ions indicate initial layer-by-layer growth, followed by multilayer growth on top of the two-monolayer film. Growth temperatures below about 400 K result in a persistent though rough layer growth up to higher coverages. From distinct maxima in the target current as a function of the azimuthal incidence angle, we deduce that growth is epitaxial and pseudomorphic.