The annotation of brain lesion images is a key step in clinical diagnosis and treatment of a wide spectrum of brain diseases. In recent years, segmentation methods based on deep learning have gained unprecedented popularity, leveraging a large amount of data with high-quality voxel-level annotations. However, due to the limited time clinicians can provide for the cumbersome task of manual image segmentation, semi-supervised medical image segmentation methods present an alternative solution as they require only a few labeled samples for training. In this paper, we propose a novel semi-supervised segmentation framework that combines improved mean teacher and adversarial network. Specifically, our framework consists of (i) a student model and a teacher model for segmenting the target and generating the signed distance maps of object surfaces, and (ii) a discriminator network for extracting hierarchical features and distinguishing the signed distance maps of labeled and unlabeled data. Besides, based on two different adversarial learning processes, a multi-scale feature consistency loss derived from the student and teacher models is proposed, and a shape-aware embedding scheme is integrated into our framework. We evaluated the proposed method on the public brain lesion datasets from ISBI 2015, ISLES 2015, and BRATS 2018 for the multiple sclerosis lesion, ischemic stroke lesion, and brain tumor segmentation respectively. Experiments demonstrate that our method can effectively leverage unlabeled data while outperforming the supervised baseline and other state-of-the-art semi-supervised methods trained with the same labeled data. The proposed framework is suitable for joint training of limited labeled data and additional unlabeled data, which is expected to reduce the effort of obtaining annotated images.