We present a new method to jointly perform deblurring and color- demosaicing of RGB images. Our method is derived following an inverse problem approach in a MAP framework. To avoid noise am- plification and allow for interpolation of missing data, we make use of edge-preserving spatial regularization and spectral regularization. We demonstrate the improvements brought by our algorithm by processing both simulated and real RGB images obtained with a Bayer's color filter and with different types of blurring.