This study addresses the nuanced challenge of estimating head translations within the context of six-degrees-of-freedom (6DoF) head pose estimation, placing emphasis on this aspect over the more commonly studied head rotations. Identifying a gap in existing methodologies, we recognized the underutilized potential synergy between facial geometry and head translation. To bridge this gap, we propose a novel approach called the head \textbf{T}ranslation, \textbf{R}otation, and face \textbf{G}eometry network (TRG), which stands out for its explicit bidirectional interaction structure. This structure has been carefully designed to leverage the complementary relationship between face geometry and head translation, marking a significant advancement in the field of head pose estimation. Our contributions also include the development of a strategy for estimating bounding box correction parameters and a technique for aligning landmarks to image. Both of these innovations demonstrate superior performance in 6DoF head pose estimation tasks. Extensive experiments conducted on ARKitFace and BIWI datasets confirm that the proposed method outperforms current state-of-the-art techniques. The code will be released.