Calcite and magnesite are important mineral constituents of the earth's crust. In aqueous environments, these carbonates typically expose their most stable cleavage plane, the (10.4) surface. It is known that these surfaces interact with a large variety of organic molecules, which can result in surface restructuring. This process is decisive for the formation of biominerals. With the development of 3D atomic force microscopy (AFM) it is now possible to image solid-liquid interfaces with unprecedented molecular resolution. However, the majority of 3D AFM studies have been focused on the arrangement of water at carbonate surfaces. Here, we present an analysis of the assembly of ethanol - an organic molecule with a single hydroxy group - at the calcite and magnesite (10.4) surfaces by using high-resolution 3D AFM and molecular dynamics (MD) simulations. Within a single AFM data set we are able to resolve both the first laterally ordered solvation layer of ethanol on the calcite surface as well as the following solvation layers that show no lateral order. Our experimental results are in excellent agreement with MD simulations. The qualitative difference in the lateral order can be understood by the differing chemical environment: While the first layer adopts specific binding positions on the ionic carbonate surface, the second layer resides on top of the organic ethyl layer. A comparison of calcite and magnesite reveals a qualitatively similar ethanol arrangement on both carbonates, indicating the general nature of this finding.