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In this Letter we present, to the best of our knowledge, the first integrated CMOS image sensor that can simultaneously perform light field and polarization imaging without the use of external filters or additional optical elements. Previous work has shown how photodetectors with two stacks of integrated metal gratings above them (called angle sensitive pixels) diffract light in a Talbot pattern to capture four-dimensional light fields. We show, in addition to diffractive imaging, that these gratings polarize incoming light and characterize the response of these sensors to polarization and incidence angle. Finally, we show two applications of polarization imaging: imaging stress-induced birefringence and identifying specular reflections in scenes to improve light field algorithms for these scenes.