The two-dimensional miscibility of 7-(2-anthryl)heptanoic acid (2A7) and myristic acid (MY) in insoluble monolayers at the air/water interface is studied at different molar ratios by recording surface pressure/ area isotherms and Brewster angle microscopy (BAM) images. The pure 2A7 dye monolayers exhibit a microaggregated polycrystalline texture, while the pure MY films show a temperature-dependent first-order main transition (L(1)/L(2)) from a fluid to a condensed state with a characteristic inner structure of the domains. The miscibility of 2A7 and MY appears to be dependent both on their molar ratio and the surface pressure, determining the phase state of the corresponding monolayers. The homogeneous distribution of dye molecules in the lipid matrix at very low 2A7 molar fractions is replaced by a progressive phase separation into stripe textures at larger 2A7 concentrations. Demixing is favored by the increase of the surface pressures as well. The results lead to the principal conclusion that components forming 2D crystalline lattices of different packing symmetries will phase separate. The conclusion about a partial miscibility in the floating 2A7/MY monolayers is in agreement with the fluorescence spectroscopic results obtained for transferred mono- and multilayers of the same compositions. BAM images of overcompressed 2A7/MY films reveal that the two components are immiscible in a 3D state.