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In image fusion tasks, images obtained from different sources exhibit distinct properties. Consequently, treating them uniformly with a single-branch network can lead to inadequate feature extraction. Additionally, numerous works have demonstrated that multi-scaled networks capture information more sufficiently than single-scaled models in pixel-level computer vision problems. Considering these factors, we propose U2Net, a spatial-spectral-integrated double U-shape network for image fusion. The U2Net utilizes a spatial U-Net and a spectral U-Net to extract spatial details and spectral characteristics, which allows for the discriminative and hierarchical learning of features from diverse images. In contrast to most previous works that merely employ concatenation to merge spatial and spectral information, this paper introduces a novel spatial-spectral integration structure called S2Block, which combines feature maps from different sources in a logical and effective way. We conduct a series of experiments on two image fusion tasks, including remote sensing pansharpening and hyperspectral image super-resolution (HISR). The U2Net outperforms representative state-of-the-art (SOTA) approaches in both quantitative and qualitative evaluations, demonstrating the superiority of our method. The code is available at https://github.com/PSRben/U2Net.