In this work, a general theoretical framework is presented to explain the formation of the phase signal in an X-ray microscope integrated with a grating interferometer, which simultaneously enables the high spatial resolution imaging and the improved image contrast. Using this theory, several key parameters of phase contrast imaging can be predicted, for instance, the fringe visibility and period, the conversion condition from the differential phase imaging (DPI) to the phase difference imaging (PDI). Additionally, numerical simulations are performed with certain X-ray optical components and imaging geometry. Results demonstrate the accuracy of this developed quantitative analysis method of X-ray phase-sensitive microscope imaging., 8 pages, 3 figures