Due to the latest progress in image sensor manufacturing technology, the emergence of a sensor equipped with an RGGB Bayer filter and a directional polarizing filter has brought significant advantages to computer vision tasks where RGB and polarization information is required. In this regard, joint chromatic and polarimetric image demosaicing is indispensable. However, as a new type of array pattern, there is no dedicated method for this challenging task. In this Letter, we collect, to the best of our knowledge, the first chromatic-polarization dataset and propose a chromatic-polarization demosaicing network (CPDNet) to address this joint chromatic and polarimetric image demosaicing issue. The proposed CPDNet is composed of the residual block and the multi-task structure with the costumed loss function. The experimental results show that our proposed methods are capable of faithfully recovering full 12-channel chromatic and polarimetric information for each pixel from a single mosaic image in terms of quantitative measures and visual quality.