The success of deep learning methods in medical image segmentation tasks usually requires a large amount of labeled data. However, obtaining reliable annotations is expensive and time-consuming. Semi-supervised learning has attracted much attention in medical image segmentation by taking the advantage of unlabeled data which is much easier to acquire. In this paper, we propose a novel dual-task mutual learning framework for semi-supervised medical image segmentation. Our framework can be formulated as an integration of two individual segmentation networks based on two tasks: learning region-based shape constraint and learning boundary-based surface mismatch. Different from the one-way transfer between teacher and student networks, an ensemble of dual-task students can learn collaboratively and implicitly explore useful knowledge from each other during the training process. By jointly learning the segmentation probability maps and signed distance maps of targets, our framework can enforce the geometric shape constraint and learn more reliable information. Experimental results demonstrate that our method achieves performance gains by leveraging unlabeled data and outperforms the state-of-the-art semi-supervised segmentation methods.