The success of deep learning in various tasks, including solving inverse problems, has triggered the need for designing deep neural networks that incorporate domain knowledge. In this paper, we design a multimodal deep learning architecture for guided image super-resolution, which refers to the problem of super-resolving a low-resolution image with the aid of a high-resolution image of another modality. The proposed architecture is based on a novel deep learning model, obtained by unfolding a proximal method that solves the problem of convolutional sparse coding with side information. We applied the proposed architecture to super-resolve near-infrared images using RGB images as side information. Experimental results report average PSNR gains of up to 2.85 dB against state-of-the-art multimodal deep learning and sparse coding models.