Learning-based deformable image registration (DIR) achieves accurate correspondences but struggles with intensity changes [1], e.g., COVID-19, where evolving ground-glass opacities, consolidations, and inflation differences alter Hounsfield distributions. We incorporate rigid anatomical guidance [2]: bone masks define rigidly-moving regions, with per-structure pre-alignment and a differentiable rigid-consistency loss constraining the field within masks while allowing flexible softtissue deformations. Using TransMorph [3] on Learn2Reg NLST thoracic CT [4] (209 volumes; 1.5 mm isotropic; 224×192×224), we compare baseline, label-only, rigid-only, and combined regimes via overlap (DSC, HD95) and plausibility metrics (volume change, HU-histogram JS divergence, negative Jacobians). Label-only achieves the strongest overlap but degrades plausibility; rigid-only significantly improves volume preservation (p = 0.003). Combined supervision balances this trade-off, significantly reducing HU deviation (p = 0.004) and negative Jacobians (p < 0.001) without significant volume change (p = 0.130), preventing rib collapse/stretching. The architecture-agnostic rigid loss is extensible to other anatomies for biomechanically plausible longitudinal CT analyses.