The structure of liquid water and 2-propanol on the (104) surface of calcite (CaCO3) was probed by frequency-modulation atomic force microscopy. The microscope tip scanned each liquid to record the tip-surface force perturbed by the liquid structure at the interface. In water, the force distribution on planes cross-sectional to the surface presents a 0.5-nm-thick checkerboard-like pattern matching the corrugated topography of the calcite surface. This provides evidence that the local water density was laterally and vertically modulated. With 2-propanol, a laterally uniform, vertically layered structure was found between the first laterally structured layer and the bulk liquid. These results are consistent with the density distributions of water and ethanol proposed in earlier X-ray and simulation studies.