We report a grazing incidence X-ray diffraction (GIXD) study df mixed Langmuir monolayers of stearic acid (ST) and a fluorinated amphiphilic molecule (FEP). The mixing behavior of the two components was investigated at two different surface pressures, 5 and 30 mN/m: The ST molecules are found to be in the L-2 mesophase at 5 mN/m and in the LS mesophase at 30 mN/m, whereas the FEP molecules appear disordered. In the mixture, the GIXD measurements, associated with previous thermodynamical and optical microscopy results, show that in the whole range of molar ratio, the two molecules are completely phase-separated, Also, we observed at 5 mN/m, relaxation in the pure ST monolayer and in the mixtures rich in ST; the tilt angle of the molecules and the rectangular distortion of the 2D-lattice decrease. By comparing mixed films and pure ST films, this relaxation could be correlated to the size of the domains.