Semi-supervised medical image segmentation offers a promising solution for large-scale medical image analysis by significantly reducing the annotation burden while achieving comparable performance. Employing this method exhibits a high degree of potential for optimizing the segmentation process and increasing its feasibility in clinical settings during translational investigations. Recently, cross-supervised training based on different co-training sub-networks has become a standard paradigm for this task. Still, the critical issues of sub-network disagreement and label-noise suppression require further attention and progress in cross-supervised training. This paper proposes a cross-supervised learning framework based on dual classifiers (DC-Net), including an evidential classifier and a vanilla classifier. The two classifiers exhibit complementary characteristics, enabling them to handle disagreement effectively and generate more robust and accurate pseudo-labels for unlabeled data. We also incorporate the uncertainty estimation from the evidential classifier into cross-supervised training to alleviate the negative effect of the error supervision signal. The extensive experiments on LA and Pancreas-CT dataset illustrate that DC-Net outperforms other state-of-the-art methods for semi-supervised segmentation. The code will be released soon.