The detailed atomic structures at the interfaces of laser-ablated epitaxial YBa2Cu3O7-x (YBCO) thin films on Y2O3 were characterized by high-resolution electron microscopy and multi-slice image simulations. Two cases of stacking sequences were found at the YBCO/Y2O3 interfaces. In the first case, the first atomic layer of the YBCO at the interface is a BaO plane, with the Ba atoms positioned 0.3 nm (projected distance) above the upper Y plane of the Y2O3. In the second case, a CuO2-like plane is the first atomic layer of the YBCO film, with the Cu atoms positioned 0.2 nm (projected distance) above the upper Y plane of the Y2O3. The images are insensitive to the oxygen arrangement at the interfaces. Close to the interface, (001) stacking faults are found in some cases, involving extra CuO and heavy-cation (Y or Ba) planes, before the perfect stacking of YBCO is established further away from the interface.