Although multi-view multi-label learning has been extensively studied, research on the dual-missing scenario, where both views and labels are incomplete, remains largely unexplored. Existing methods mainly rely on contrastive learning or information bottleneck theory to learn consistent representations under missing-view conditions, but loss-based alignment without explicit structural constraints limits the ability to capture stable and discriminative shared semantics. To address this issue, we introduce a more structured mechanism for consistent representation learning: we learn discrete consistent representations through a multi-view shared codebook and cross-view reconstruction, which naturally align different views within the limited shared codebook embeddings and reduce feature redundancy. At the decision level, we design a weight estimation method that evaluates the ability of each view to preserve label correlation structures, assigning weights accordingly to enhance the quality of the fused prediction. In addition, we introduce a fused-teacher self-distillation framework, where the fused prediction guides the training of view-specific classifiers and feeds the global knowledge back into the single-view branches, thereby enhancing the generalization ability of the model under missing-label conditions. The effectiveness of our proposed method is thoroughly demonstrated through extensive comparative experiments with advanced methods on five benchmark datasets. Code is available at https://github.com/xuy11/SCSD.