Thanks to the latest progress in image sensor manufacturing technology, the emergence of the single-chip polarized color sensor is likely to bring advantages to computer vision tasks. Despite the importance of the sensor, joint chromatic and polarimetric demosaicing is the key to obtaining the high-quality RGB-Polarization image for the sensor. Since the polarized color sensor is equipped with a new type of chip, the demosaicing problem cannot be currently well-addressed by former methods. In this paper, we propose a joint chromatic and polarimetric demosaicing model to address this challenging problem. To solve this non-convex problem, we further present a sparse representation-based optimization strategy that utilizes chromatic information and polarimetric information to jointly optimize the model. In addition, we build an optical data acquisition system to collect an RGB-Polarization dataset. Results of both qualitative and quantitative experiments have shown that our method is capable of faithfully recovering full 12-channel chromatic and polarimetric information for each pixel from a single mosaic input image. Moreover, we show that the proposed method can perform well not only on the synthetic data but the real captured data.