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Given a low-resolution (LR) image, multi-modal image super-resolution (MISR) aims to find the high-resolution (HR) version of this image with the guidance of an HR image from another modality. In this paper, we use a model-based approach to design a new deep network architecture for MISR. We first introduce a novel joint multi-modal dictionary learning (JMDL) algorithm to model cross-modality dependency. In JMDL, we simultaneously learn three dictionaries and two transform matrices to combine the modalities. Then, by unfolding the iterative shrinkage and thresholding algorithm (ISTA), we turn the JMDL model into a deep neural network, called deep coupled ISTA network. Since the network initialization plays an important role in deep network training, we further propose a layer-wise optimization algorithm (LOA) to initialize the parameters of the network before running back-propagation strategy. Specifically, we model the network initialization as a multi-layer dictionary learning problem, and solve it through convex optimization. The proposed LOA is demonstrated to effectively decrease the training loss and increase the reconstruction accuracy. Finally, we compare our method with other state-of-the-art methods in the MISR task. The numerical results show that our method consistently outperforms others both quantitatively and qualitatively at different upscaling factors for various multi-modal scenarios. [ABSTRACT FROM AUTHOR]