Online HD map construction serves as a critical infrastructure for autonomous driving, providing precise geometric and semantic priors for downstream planning modules. While existing methods have improved accuracy, they remain challenged by disordered vectorized sequences and topological distortions caused by noisy sensor inputs and fragmented decoding mechanisms. To address these limitations, we propose Hierarchical Dual-Path Framework for Robust HD Map Construction via Median-Enhanced Attention and Geometric-Semantic Interaction(HDP-Map), a dual-path framework featuring hierarchical semantic-geometric interaction with two key innovations: Median-enhanced Multi-scale Spatial Attention (M2SA): A noise-robust feature fusion module integrating differentiable median pooling and multi-scale convolutional operations, effectively suppressing environmental interference while enhancing local discriminability for elongated structures like lane markings. Hierarchical Interaction Decoder: A transformer-based architecture that synchronously optimizes global topology consistency and local geometric continuity through bidirectional refinement of semantic-level queries and topology-level queries. Extensive experiments demonstrate state-of-the-art performance on nuScenes and Argoverse2 benchmarks: HDP-Map achieves 67.3% mAP on nuScenes, surpassing MapTR by +5.0% . HDP-Mapv2 attains 69.4% mAP on Argoverse2, outperforming MapTRv2 by +5.8% with 41% fewer topological fractures. The framework provides a deployment-friendly solution for real-time HD map construction, balancing precision and efficiency in complex urban scenarios.