Mitochondria segmentation in electron microscopy (EM) images greatly benefits from unsupervised domain adaptation (UDA) techniques, which enable the analysis of neuronal structures and functions without time-consuming manual annotations. In this work, we propose a content-aware UDA method for mitochondria segmentation in EM images that synergistically combines established techniques in a novel manner, effectively preserving delicate mitochondrial structures during style transfer, enhancing the capture of fine details and contextual information with improved parameter efficiency, and ensuring the geometric continuity of predictions in the target modality. First, our model preserves delicate mitochondrial structures during style transfer by integrating pixel-level, perceptual, and 3D structural information. Second, we propose a novel residual asymmetric convolution (RAC) module to enhance the simultaneous capture of fine mitochondria structures and contextual information. Third, we utilize morphological operations to refine pseudo-labels generated by our inter-slice residual differences mechanism, further guiding the geometric continuity of predictions in the target modality. Extensive experiments on two representative datasets demonstrate that our method outperforms several state-of-the-art UDA methods.