Segmenting clouds and their shadows is a critical challenge in remote sensing image processing. The shape, texture, lighting conditions, and background of clouds and their shadows impact the effectiveness of cloud detection. Currently, architectures that maintain high resolution throughout the entire information-extraction process are rapidly emerging. This parallel architecture, combining high and low resolutions, produces detailed high-resolution representations, enhancing segmentation prediction accuracy. This paper continues the parallel architecture of high and low resolution. When handling high- and low-resolution images, this paper employs a hybrid approach combining the Transformer and CNN models. This method facilitates interaction between the two models, enabling the extraction of both semantic and spatial details from the images. To address the challenge of inadequate fusion and significant information loss between high- and low-resolution images, this paper introduces a method based on ASMA (Axial Sharing Mixed Attention). This approach establishes pixel-level dependencies between high-resolution and low-resolution images, aiming to enhance the efficiency of image fusion. In addition, to enhance the effective focus on critical information in remote sensing images, the AGM (Attention Guide Module) is introduced, to integrate attention elements from original features into ASMA, to alleviate the problem of insufficient channel modeling of the self-attention mechanism. Our experimental results on the Cloud and Cloud Shadow dataset, the SPARCS dataset, and the CSWV dataset demonstrate the effectiveness of our method, surpassing the state-of-the-art techniques for cloud and cloud shadow segmentation.