Accurate medical image segmentation is essential for reliable clinical diagnosis, treatment planning, and outcome evaluation. However, existing transformer- and CNN-based approaches often fail to jointly capture long-range contextual dependencies and emphasize task-relevant structures, limiting their ability to delineate complex anatomical boundaries. To address these issues, we propose CCASNet, a dual-channel spatial modeling framework that unifies global structural reasoning and fine-grained representation refinement. Specifically, CCASNet introduces a dual-channel complementary attention mechanism, in which (i) a Criss-Cross Attention branch captures long-range dependencies and ensures global structural coherence with reduced complexity, while (ii) a Channel-Spatial Attention branch adaptively emphasizes diagnostically relevant regions and suppresses background noise. Unlike previous works that simply apply attention in a single dimension, our design explicitly models global – local complementarity, enabling robust delineation of complex anatomical boundaries. This complementary design enables CCASNet to simultaneously achieve global consistency and local precision. Extensive evaluations on Synapse and ACDC datasets demonstrate that CCASNet consistently outperforms competitive baselines, achieving an average Dice score of 85.62% (+8.14% over TransUNet) and reducing HD95 to 13.36. These results highlight the robustness, efficiency, and clinical applicability of the proposed framework.