In this paper, we present a modified transmission digital holographic microscope that can be used to image the state of polarization. The resulting device, called polarization digital holographic microscope (Pol-DHM), records in off-axis geometry the interference between two orthogonally polarized reference waves and the object wave transmitted by a microscopic sample and magnified by a microscope objective. A CCD camera records the resulting hologram. Using a single hologram, we reconstruct separately the amplitude and phase of two wave fronts, which are used to represent the object wave's state of polarization, represented by the azimuth and the phase difference associated to the polarization ellipse. ne proposed method is illustrated with two applications. The first application is to use a 10-times magnification microscope objective to measure the bireftingence induced by internal stresses in transparent materials such as a bended optical fiber. The second application is to use a 20-times microscope objective to image the state of polarization of a thin concrete sample and reveals birefringent properties of the different aggregates found in the concrete.