Hierarchical multi-label classification (HMLC) is essential for modeling complex and structured label dependencies in image analysis domains such as remote sensing and medical diagnostics. Despite advances in deep learning, existing methods face key limitations in handling instances belonging to multiple hierarchical paths, fully exploiting hierarchical information, and leveraging unlabeled data. This paper introduces HELM, a novel hierarchical multi-label learning framework that overcomes these limitations. HELM introduces: (i) hierarchy-specific class tokens to capture internal label interactions within complex multi-path hierarchies; (ii) graph convolutional networks to encode hierarchical structures and generate hierarchy-aware embeddings; and (iii) a semi-supervised framework that leverages unlabeled data to enhance discriminative power when labeled data is scarce. To facilitate advances in HMLC research, where image datasets are in short supply, we additionally construct HMLC versions of eight existing multi-label classification datasets from remote sensing and medical domains. In comprehensive evaluations, HELM outperforms multi-label classification baselines by an average of 9.3