The composite structure comprising case and skirt of a solid rocket motor (SRM) undergoes aging over prolonged periods of storage, consequently compromising reliability of the case structure of SRM. This study conducted an accelerated hot-humid aging test on typical materials of the skirt composite structure to assess its mechanical properties throughout the aging process. Additionally, microstructure parameters of the epoxy resin material presenting at the interface of the composite structure, i.e., the vulnerable spot, were characterized. Subsequent to the test, a cross-scale comparative analysis was performed to evaluate material damage at the composite structure’s interface. The results revealed that during accelerated aging, the epoxy resin matrix exhibited a gradual transition to a gully-shaped surface, with increasing surface damage severity correlated with the aging duration. The continuous rise in three-dimensional surface roughness contributed to material embrittlement and diminished toughness, resulting in a decline in the mechanical properties at interface of the composite structure. Analysis through Fourier transform infrared spectroscopy testing and X-ray photoelectron spectroscopy analysis further elucidated molecular-level damage to the epoxy resin matrix. As aging progressed, chemical reactions among the elemental groups were observed, reflecting potential oxidative crosslinking or decomposition reactions. Finally, a correlation analysis involving macroscopic and microscopic parameters was conducted to explain the cross-scale damage mechanism at the interface of the case composite structure.