Solid solutions of α-Cr2O3 and α-Fe2O3 are novel oxide semiconductors exhibiting narrower band gaps than those of the end members. We have investigated the heteroepitaxial growth and crystalline structure of pulsed-laser deposited α-(CrxFe1-x)2O3 films on c-plane sapphire substrates. Under the growth condition optimized for α-Fe2O3, reflection high-energy electron diffraction intensity oscillations were observable for both α-Fe2O3 and α-Cr2O3, enabling us to control film thickness in a layer-by-layer fashion. The composition dependence of the epitaxial structures, including phase purity, orientation, strain, and in-plane rotation domain, was characterized by X-ray diffraction to reveal a defect-free composition range (0 ≤x ≤0.50). The films with 0.60 ≤x ≤1 were found to have 180°-rotation domains. The absorption spectra of α-(Cr0.50Fe0.50)2O3 solid solution (corundum) and superlattice (nominally composed ilmenite) films are compared with those of end members and an α-Fe2O3/α-Cr2O3 bilayer film to elucidate the origin of the band-gap narrowing.