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Medical 3D scans and reports are inherently hierarchical, with diagnostic cues concentrated in specific anatomical regions across multiple levels of organization. Yet, most medical vision-language models ignore this structure and fail to focus on clinically relevant anatomy. We introduce MedHiVE, which combines hierarchical vision-language Soft Mixture-of-Experts (SMoE) with contrastive learning to jointly model fine-grained anatomy and global scan context. To our knowledge, MedHiVE is the first framework to route both vision and text tokens through a two-level SMoE hierarchy organized by anatomical scale, coupling this with report-derived anatomy-level contrastive alignment for 3D medical imaging. This replaces the direct region-text alignment of statically pooled features and vision-only hierarchical routing of prior work with dynamic, slot-based cross-modal information flow across anatomical scales. MedHiVE operates via a two-level, learnable token-routing mechanism, where local image and text features are first routed through a local SMoE and then fused by a global SMoE into unified multimodal representations. Contrastive learning aligns both anatomy-level and global vision-language representations in a unified space. Pre-trained on 25,000+ CT scans with anatomical supervision, MedHiVE consistently surpasses 11 state-of-the-art methods across 6 datasets on 3 tasks: segmentation, classification, and detection, demonstrating the importance of hierarchical modeling. The code for MedHiVE is at github.com/szczurek-lab/MedHiVE.