Semi-supervised learning has garnered significant interest as a method to alleviate the burden of data annotation. Recently, semi-supervised medical image segmentation has garnered significant interest that can alleviate the burden of densely annotated data. Substantial advancements have been achieved by integrating consistency-regularization and pseudo-labeling techniques. The quality of the pseudo-labels is crucial in this regard. Unreliable pseudo-labeling can result in the introduction of noise, leading the model to converge to suboptimal solutions. To address this issue, we propose learning from reliable pseudo-labels. In this paper, we tackle two critical questions in learning from reliable pseudo-labels: which pseudo-labels are reliable and how reliable are they? Specifically, we conduct a comparative analysis of two subnetworks to address both challenges. Initially, we compare the prediction confidence of the two subnetworks. A higher confidence score indicates a more reliable pseudo-label. Subsequently, we utilize intra-class similarity to assess the reliability of the pseudo-labels to address the second challenge. The greater the intra-class similarity of the predicted classes, the more reliable the pseudo-label. The subnetwork selectively incorporates knowledge imparted by the other subnetwork model, contingent on the reliability of the pseudo labels. By reducing the introduction of noise from unreliable pseudo-labels, we are able to improve the performance of segmentation. To demonstrate the superiority of our approach, we conducted an extensive set of experiments on three datasets: Left Atrium, Pancreas-CT and Brats-2019. The experimental results demonstrate that our approach achieves state-of-the-art performance. Code is available at: https://github.com/Jiawei0o0/mutual-learning-with-reliable-pseudo-labels.