Accurate breast ultrasound (BUS) image segmentation is crucial for precise diagnosis and surgical planning, but it remains challenging largely due to the scarcity of labeled BUS images. Semi-supervised methods show promise by leveraging pseudo-labels to mitigate reliance on large-scale annotations. However, their performance is highly dependent on the quality of pseudo-labels, which is difficult to guarantee in BUS images due to inherent complexities such as low contrast, speckle noise, and artifacts. Previous studies primarily focus on refining pseudo-labels in one way or the other, or introducing auxiliary supervision; yet they overlook the potential of harnessing intrinsic and inherent pixel relations to enhance the robustness of semi-supervised segmentation. In this paper, we present a novel relation-aware semi-supervised model for BUS image segmentation, which is composed of two innovative components: an adjacent relation propagation (ARP) module and a cross-layer relation alignment (CRA) module, for comprehensively explore pixel relations to improve segmentation performance. The ARP propagates relations among adjacent pixels to reinforce the collaborative prediction of correlated pixels and enhance the model's awareness of local semantic consistency. The CRA aligns cross-layer pixel relations, employing deep-layer guidance to rectify erroneous correlations in shallow layers for noise suppression, while integrating multi-scale contexts to enable robust segmentation of lesions with varying sizes. Extensive experiments on two representative BUS datasets under various labeling conditions demonstrate the superiority of our method to the SOTAs. Codes will be released upon publication.