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The guideline of “as low as reasonably achievable” (ALARA) for radiation dose has attracted attention to sparse-view spectral computed tomography (CT) imaging. Any missing scanning view in any energy will reduce the quality of image reconstruction and material decomposition. Recently, a series of achievements have been made in optimizing spectral CT imaging based on traditional iterative models or deep learning methods. However, these works are independent or simply coupled, often neglecting the dependency relationships in spectral CT imaging. Moreover, interpretability and generalization ability are still the challenges facing the existing methods. Therefore, we combine the advantages of traditional models and deep learning methods to propose an interpretable hybrid-domain integrative transformer iterative network (HITI-Net) model for synchronously optimizing spectral CT reconstruction and material decomposition of sparse-view measurements. The model fully utilizes prior information in the fields of projection, image, and material while introducing the vision transformer to learn global and long-range image information interactions. Then, the interpretable objective function is solved by the alternating directions method of multipliers (ADMMs) and further optimized the network structure according to the derived expression. In addition, hybrid-domain sparse regularization terms and balance parameters are designed to adaptively learn during the training phase to enhance the generalization ability of the HITI-Net. In simulation and real preclinical experiments, the imaging results of HITI-Net are superior to other comparison methods, with more small features and sharp edges.