Thin-walled aerospace structures are predominately modeled as plates and shells in the aerospace sector due to their superior strength-to-weight ratios. This study presents an inverse finite element method (iFEM) framework for strain-based structural health monitoring (SHM) applications of aerospace structures that can be modeled as thin-walled members. Based on the kinematic assumptions of Discrete Kirchhoff Theory (DKT), the inverse formulation enables accurate, real-time full-field shape sensing for thin plate and shell structures. To undertake inverse analysis of complex and built-up structures, the formulation is systematically extended to include drilling degrees of freedom (DOFs), ensuring both rotational compatibility and numerical stability of the inverse thin shell element. A rigorous numerical validation is carried out using a series of benchmark problems that encompass in-plane, transverse, and general loading conditions representative of aerospace structural applications. The robustness of the inverse formulation is further evaluated by reconstructing displacements in real-world scenarios that utilize sparse sensor layouts. The full-field shape sensing capability enables early identification and precise quantification of structural anomalies and supports proactive maintenance interventions to ensure continued structural integrity throughout the intended lifespan. Additionally, a comprehensive damage assessment framework is implemented to detect material discontinuities (such as cracks or voids) and to evaluate material degradation resulting from the cyclic loading conditions typical of aerospace structures. A strain-based damage index derived from the reconstructed strain fields is used to enable effective damage detection and prognosis, which enables the implementation of condition-based maintenance strategies and real-time adaptive load management. The iFEM framework provides a reliable tool for health assessment and monitoring, ensuring sustained structural integrity in thin-walled aerospace systems throughout their service life.