Cracks are common defects in building structures, and timely detection is essential for safety. However, segmenting tiny cracks faces challenges such as significant background interference, insufficient segmentation accuracy, and high computational complexity. To tackle these issues, we propose a parallel dual-encoding crack segmentation model (CMC-Net) that combines convolutional neural network (CNN) and Mamba, aimed at achieving high-precision segmentation of tiny cracks. Firstly, to achieve linear computational complexity while detecting a few crack pixels in a large background, we designed a global feature extraction branch with magnification capabilities based on Mamba. Additionally, we incorporated residual and multi-scale operations to enhance the perception of tiny cracks in the model. Secondly, we designed a multi-scale interactive alignment module (MSIA) to fuse and align the semantic information features that exhibit significant differences between the two branches, thereby enhancing the correlation between features from different branches. Finally, we compared the proposed method with ten advanced models on two public datasets. The experimental results show that CMC-Net performs well in tiny crack segmentation and reducing background interference, achieving an F1 score of 82.4% and a MPA of 92.02% on the Volker dataset. Code can be obtained from https://github.com/beiye223/CMC-Net .