Sophisticated segmentation of the craniomaxillofacial bones (the mandible and maxilla) in computed tomography (CT) is essential for diagnosis and treatment planning for craniomaxillofacial surgeries. Conventional manual segmentation is time-consuming and challenging due to intrinsic properties of craniomaxillofacial bones and head CT such as the variance in the anatomical structures, low contrast of soft tissue, and artifacts caused by metal implants. However, data-driven segmentation methods, including deep learning, require a large consistent dataset, which creates a bottleneck in their clinical applications due to limited datasets. In this study, we propose a deep learning approach for the automatic segmentation of the mandible and maxilla in CT images and enhanced the compatibility for multi-center datasets. Four multi-center datasets acquired by various conditions were applied to create a scenario where the model was trained with one dataset and evaluated with the other datasets. For the neural network, we designed a hierarchical, parallel and multi-scale residual block to the U-Net (HPMR-U-Net). To evaluate the performance, segmentation with in-house dataset and with external datasets from multi-center were conducted in comparison to three other neural networks: U-Net, Res-U-Net and mU-Net. The results suggest that the segmentation performance of HPMR-U-Net is comparable to that of other models, with superior data compatibility.