We demonstrate a quantitative reflection-phase microscope based on time-varying speckle-field illumination. Due to the short spatial coherence length of the speckle field, the proposed imaging system features superior lateral resolution, 520 nm, as well as high-depth selectivity, 1.03 μm. Off-axis interferometric detection enables wide-field and single-shot imaging appropriate for high-speed measurements. In addition, the measured phase sensitivity of this method, which is the smallest measurable axial motion, is more than 40 times higher than that available using a transmission system. We demonstrate the utility of our method by successfully distinguishing the motion of the top surface from that of the bottom in red blood cells. The proposed method will be useful for studying membrane dynamics in complex eukaryotic cells.