Mineral-water interfaces play an important role in many natural as well as technological fields. Fundamental properties of these interfaces are governed by the presence of the interfacial water and its specific structure at the surface. Calcite is particularly interesting as a dominant rock-forming mineral in the earth's crust. Here, we combine atomic force microscopy, sum-frequency generation spectroscopy, and molecular dynamics simulations to determine the position and orientation of the water molecules in the hydration layers of the calcite surface with high resolution. While atomic force microscopy provides detailed information about the position of the water molecules at the interface, sum-frequency generation spectroscopy can deduce the orientation of the water molecules. Comparison of the calcite-water interface to the interfaces of magnesite-water, magnesite-ethanol, and calcite-ethanol reveals a comprehensive picture with opposite water orientations in the first and second layer of the interface, which is corroborated by the molecular dynamics simulations.