In the last two decades, the use of synthetic aperture radar (SAR) for remote sensing purposes has significantly developed due to improvements in the quality and the availability of the images. Two powerful SAR techniques, namely, polarimetry and interferometry, have further increased the range of applications of the sensed data. Using polarimetry, geometrical properties and geophysical parameters, such as shape, roughness, texture, and moisture content, can be retrieved with considerable accuracy, while interferometric information may be used to extract vertical information with accuracy less than 1 cm. In this paper, the potential of using joint polarimetry and interferometry techniques in SAR data (PolInSAR) for the purpose of SAR image classification is investigated. To achieve this goal, we extend a covariance symmetry detection framework to the PolInSAR scenario. The proposed approach will be shown to be able to exploit the peculiar structures of the covariance matrices of PolInSAR images to discriminate structures within the image. Results using real-SAR data are presented to validate the effectiveness of the proposed approach.