Based on pseudo-labels, voxel-wise contrastive learning (VCL) is a prominent approach designed to learn effective feature representations for semi-supervised medical image segmentation. However, in multi-organ segmentation (MoS), the complex anatomical structures of certain organs often lead to many unreliable pseudo-labels. Directly applying VCL can introduce confirmation bias, resulting in poor segmentation performance. A common practice is to first transform these unreliable pseudo-labels into complementary ones, which represent classes that voxels are least likely to belong to, and then push voxels away from the generated complementary labels. However, we find that this approach may fail to allow voxels with unreliable pseudo-labels (unreliable voxels) to fully benefit from the advantages of VCL. In this paper, we propose DVCL, a novel distance-aware VCL method for semi-supervised MoS. DVCL is based on the observation that unreliable voxels, which may not form discriminative feature boundaries, still form clear clusters. Hence, voxels close to each other in the feature space ('neighbors') likely belong to the same semantic class, while distant ones ('outsiders') likely belong to different classes. In DVCL, we first identify neighbors and outsiders for all unreliable voxels, and then pull their neighbors into the same clusters while pushing outsiders away. In this way, unreliable voxels can learn more discriminative features, thereby fully enjoying the advantages of VCL. However, DVCL itself will inevitably introduce the problem of noisy neighbors and outliers. To address these challenges, we further propose a neighbor partitioning strategy and a query outlier strategy to provide more stable feature representations for DVCL. Extensive experiments demonstrate the effectiveness of our method.