Both limited annotation and domain shift are prevalent challenges in medical image segmentation. Traditional semi-supervised segmentation and unsupervised domain adaptation methods address one of these issues separately. However, the coexistence of limited annotation and domain shift is quite common, which motivates us to introduce a novel and challenging scenario: Mixed Domain Semi-supervised medical image Segmentation (MiDSS), where limited labeled data from a single domain and a large amount of unlabeled data from multiple domains. To tackle this issue, we propose the UST-RUN framework, which fully leverages intermediate domain information to facilitate knowledge transfer. We employ Unified Copy-paste (UCP) to construct intermediate domains, and propose a Symmetric GuiDance training strategy (SymGD) to supervise unlabeled data by merging pseudo-labels from intermediate samples. Subsequently, we introduce a Training Process aware Random Amplitude MixUp (TP-RAM) to progressively incorporate style-transition components into intermediate samples. To generate more diverse intermediate samples, we further select reliable samples with high-quality pseudo-labels, which are then mixed with other unlabeled data. Additionally, we generate sophisticated intermediate samples with high-quality pseudo-labels for unreliable samples, ensuring effective knowledge transfer for them. Extensive experiments on four public datasets demonstrate the superiority of UST-RUN. Notably, UST-RUN achieves a 12.94% improvement in Dice score on the Prostate dataset. Our code is available at https://github.com/MQinghe/UST-RUN