Multiple sclerosis (MS) and neuromyelitis optica spectrum disorder (NMOSD) are demyelinating disorders of the central nervous system, exhibiting highly overlapping imaging features that often lead to misdiagnosis. The anterior visual pathway (AVP), as a critical lesion site, plays an essential role in early diagnosis. However, the AVP’s elongated anatomical structure and subtle lesion areas make it challenging to capture its characteristics. Yet, the length of the anatomical structure and the localized subtle lesions are precisely the key factors in distinguishing between the two diseases. To overcome this limitation, we propose a multi-task model, CM-MNet, which employs a novel coordinate-space-aware Mamba backbone encoder. This encoder extracts subtle pathological tissue structures within the anatomical coordinates of the AVP that are difficult to detect in MS and NMOSD while preserving the Elongated structural continuity of the AVP. In the decoding phase, a morphology-based post-processing method is introduced, incorporating medical prior knowledge to classify the segmentation results into primary and secondary lesion regions, and extracting weighted lesion features to assist classification. Experimental results demonstrate that the AVP-based multi-task model significantly outperforms both single-task networks and existing multi-task frameworks, thereby validating its clinical applicability. By incorporating the AVP into the diagnostic process, this model significantly enhances diagnostic accuracy and interpretability, offering distinct advantages over traditional diagnostic methods.