We report the molecular beam epitaxy of Bi1−xSbx thin films (0 ≤ x ≤ 1) on sapphire (0001) substrates using a thin (Bi,Sb)2Te3 buffer layer. The characterization of the films using reflection high energy diffraction, x-ray diffraction, atomic force microscopy, and scanning transmission electron microscopy reveals the epitaxial growth of films of reasonable structural quality. This is further confirmed via x-ray diffraction pole figures that determine the epitaxial registry between the thin film and the substrate. We further investigate the microscopic structure of thin films via Raman spectroscopy, demonstrating how the vibrational modes vary as the composition changes and discussing the implications for the crystal structure. We also characterize the samples using electrical transport measurements.