Accurate characterization of hippocampal substructure is crucial for detecting subtle structural changes and identifying early neurodegenerative biomarkers. However, high inter-subject variability and complex folding pattern of human hippocampus hinder consistent cross-subject and longitudinal analysis. Most existing approaches rely on subject-specific modelling and lack a stable intrinsic coordinate system to accommodate anatomical variability, which limits their ability to establish reliable inter- and intra-individual correspondence. To address this, we propose HippMetric, a skeletal representation (s-rep)-based framework for hippocampal substructural morphometry and point-wise correspondence across individuals and scans. HippMetric builds on the Axis-Referenced Morphometric Model (ARMM) and employs a deformable skeletal coordinate system aligned with hippocampal anatomy and function, providing a biologically grounded reference for correspondence. Our framework comprises two core modules: a skeletal-based coordinate system that respects the hippocampus' conserved longitudinal lamellar architecture, in which functional units (lamellae) are stacked perpendicular to the long-axis, enabling anatomically consistent localization across subjects and time; and individualized s-reps generated through surface reconstruction, deformation, and geometrically constrained spoke refinement, enforcing boundary adherence, orthogonality and non-intersection to produce mathematically valid skeletal geometry. Extensive experiments on two international cohorts demonstrate that HippMetric achieves higher accuracy, reliability, and correspondence stability compared to existing shape models.