We report on the lattice and band structures of complete solid-solution β-(AlxGa1-x)2O3 (x = 0-1) films that were epitaxially grown on β-Ga2O3 (100) substrates by using oxygen-radical-assisted pulsed-laser deposition. We found that oxygen-plasma treatment of the substrate surface was the key to achieving a two-dimensional growth mode of not only β-Ga2O3 but also θ-Al2O3 with the β-gallia structure. The band gap of β-(AlxGa1-x)2O3 increased from 4.51 ± 0.02 eV (x = 0) to 6.91 ± 0.02 eV (x = 1). The x-dependence of the (100) spacing and band gap showed the anomalous bowing behavior, as the curvatures changed around x ∼0.5. This tendency was ascribed to the different arrangements of the Al and Ga cations along their tetrahedral and octahedral site preference in the β-gallia structure. We also fabricated a short-period superlattice composed of θ-Al2O3 and β-Ga2O3 layers to verify the sharp interface from the X-ray diffraction profile.