Regularizing the training of deformable image registration networks (DIR) with anatomically motivated loss functions is essential for ensuring biomechanically plausible deformations, particularly in intra-patient longitudinal studies involving rigid structures such as bones. In this work, we propose a novel semi-supervised approach that combines conventional label-based supervision with direct supervision of the deformation field using transformation parameters from preliminary conventional bone-to-bone registration. This combined approach enforces anatomical consistency by integrating rigid priors into the training process, improving the physical plausibility of the deformation field. Our method is evaluated on thoracic CT scans from the NLST dataset, with a focus on rib alignment. Compared to baseline and label-only models, the combined supervision model achieves a better trade-off between segmentation accuracy and deformation plausibility, reducing volume changes (by 34%) and the occurrence of non-physical deformations (negJ reduction by 53%). As an ablation study, we also evaluate a rigid-only supervision model. These findings highlight the benefit of integrating anatomical priors into DIR training and open new avenues for anatomy-aware registration strategies. The code and data are available at: https://github.com/lukasf98/semi-supervised-rigid-supervision