Surface X-ray diffraction was applied to study structure of the fluorite-silicon interface forming upon epitaxial growth of CaF2 on Si(001) surface kept at 750 degrees C. Samples with CaF2 coverage of 1.5-4 (110)-monolayers were grown and in-situ characterized using synchrotron radiation. The 3 x 1-like surface reconstruction was observed in agreement with the previous studies by electron diffraction. Interestingly, a well pronounced splitting of the fractional x 1/3 reflections was revealed. This splitting was ascribed to the effect of antiphase domain boundaries in the row-like structure of the interface layer. The in-plane integrated intensities were used to reconstruct two-dimensional atomic structure of the high-temperature CaF2/Si(001) interface.