We successfully achieved the growth of a stacked layer composed of β-(AlxGa1−x)2O3/β-(InyGa1−y)2O3 on a (010) β-Ga2O3 substrate using mist chemical vapor deposition (CVD). X-ray diffraction and reciprocal space mapping analyses were conducted, elucidating that the multilayer structure of the β-(AlxGa1−x)2O3/β-(InyGa1−y)2O3 thin film exhibited excellent crystallinity and coherent growth. Scanning transmission electron microscopy further revealed a continuous atomic arrangement at the heterointerface of β-(AlxGa1−x)2O3/β-(InyGa1−y)2O3. Furthermore, the bandgap values of β-(AlxGa1−x)2O3 and β-(InyGa1−y)2O3 thin films were determined to be 5.21 and 4.62 eV, respectively, through electron energy-loss spectroscopy. Notably, a slight broadening was observed in the bandgap transition at the interface of β-(AlxGa1−x)2O3/β-(InyGa1−y)2O3. Energy dispersive x-ray spectroscopy analysis indicated that this phenomenon could be attributed to the diffusion of In into the β-(AlxGa1−x)2O3 thin film layer. These results support mist CVD as a promising growth technique for developing β-Ga2O3-based heterojunction devices.