Cloud and cloud shadow segmentation is one of the most important issues in remote sensing image processing. Most of the remote sensing images are very complicated. In this work, a dual-branch model composed of transformer and convolution network is proposed to extract semantic and spatial detail information of the image, respectively, to solve the problems of false detection and missed detection. To improve the model's feature extraction, a mutual guidance module (MGM) is introduced, so that the transformer branch and the convolution branch can guide each other for feature mining. Finally, in view of the problem of rough segmentation boundary, this work uses different features extracted by the transformer branch and the convolution branch for decoding and repairs the rough segmentation boundary in the decoding part to make the segmentation boundary clearer. Experimental results on the Landsat-8, Sentinel-2 data, the public dataset high-resolution cloud cover validation dataset created by researchers at Wuhan University (HRC_WHU), and the public dataset Spatial Procedures for Automated Removal of Cloud and Shadow (SPARCS) demonstrate the effectiveness of our method and its superiority to the existing state-of-the-art cloud and cloud shadow segmentation approaches.