Significance: The hallmarks of digital holographic microscopy (DHM) compared with other quantitative phase imaging (QPI) methods are high speed, accuracy, spatial resolution, temporal stability, and polarization-sensitivity (PS) capability. The above features make DHM suitable for real-time quantitative PS phase imaging in a broad number of biological applications aimed at understanding cell growth and dynamic changes occurring during physiological processes and/or in response to pharmaceutical agents. Aim: The insertion of a Fresnel biprism (FB) in the image space of a light microscope potentially turns any commercial system into a DHM system enabling QPI with the five desired features in QPI simultaneously: high temporal sensitivity, high speed, high accuracy, high spatial resolution, and PS. To the best of our knowledge, this is the first FB-based DHM system providing these five features all together. Approach: The performance of the proposed system was calibrated with a benchmark phase object. The PS capability has been verified by imaging human U87 glioblastoma cells. Results: The proposed FB-based DHM system provides accurate phase images with high spatial resolution. The temporal stability of our system is in the order of a few nanometers, enabling live-cell studies. Finally, the distinctive behavior of the cells at different polarization angles (e.g., PS capability) can be observed with our system. Conclusions: We have presented a method to turn any commercial light microscope with monochromatic illumination into a PS QPI system. The proposed system provides accurate quantitative PS phase images in a new, simple, compact, and cost-effective format, thanks to the low cost (a few hundred dollars) involved in implementing this simple architecture, enabling the use of this QPI technique accessible to most laboratories with standard light microscopes.