The local morphology and composition of mixed, two-dimensional monomolecular films (Langmuir monolayers) is studied via model calculations and investigated experimentally. The monolayers are in a typical Langmuir-Blodgett transfer configuration (Langmuir wetting), where they cover the plane water surface, the aqueous meniscus, and the solid substrate surface. They are inspected via transfer fluorescence microscopy in the region adjacent to the three-phase line where the layers touch the substrate. The observations are performed during the continuous hydrophilic transfer onto the solid substrate; i.e., the experiments probe a steady state situation. The monolayers consist of amphiphilic lipid molecules with small amounts of fluorescing dye, thus representing binary solvent/solute mixtures. Due to the different monolayer environment (e.g., additional adhesive interactions on the substrate), the mixing behavior of floating and deposited monolayers is different. This difference induces local morphological and constitutional variations (domain melting, solute pileup, etc.) in the floating monolayer section in front of the three-phase line. The data are interpreted with model calculations analogous to the description of well-known three-dimensional thermotropic solidification processes in binary alloys. In this analogy, the deposited monolayer section represents the solid alloy and the floating part of the monolayer replaces the liquid alloy. The three-phase line corresponds to the solid/liquid interface of the three-dimensional system, and the different monolayer environment acts comparable to the different temperatures in the three-dimensional analogon. The model predicts local dye concentration variations and various details on local morphological alterations. Comprehensive experimental results qualitatively and quantitatively corroborate the proposed model. The investigations show that Langmuir monolayers are excellently suited to study solidification phenomena, morphological alterations, and the mixing properties of two-dimensional systems.