Limited labeled data hinder the application of deep learning in medical domain. In clinical practice, there are sufficient unlabeled data that are not effectively used, and semi-supervised learning (SSL) is a promising way for leveraging these unlabeled data. However, existing SSL methods ignore frequency domain and region-level information and it is important for lesion regions located at low frequencies and with significant scale changes. In this paper, we introduce two consistency regularization strategies for semi-supervised medical image segmentation, including frequency domain consistency (FDC) to assist the feature learning in frequency domain and multi-granularity region similarity consistency (MRSC) to perform multi-scale region-level local context information feature learning. With the help of the proposed FDC and MRSC, we can leverage the powerful feature representation capability of them in an effective and efficient way. We perform comprehensive experiments on two datasets, and the results show that our method achieves large performance gains and exceeds other state-of-the-art methods.