The inversion of logging-while-drilling azimuthal electromagnetic measurements is essential for geosteering in horizontal wells and optimizing reservoir development. Conventional fixed-layer inversion models lack adaptability to dynamically varying formations, resulting in limited applicability and a trade-off between accuracy and efficiency. This study introduces a trans-layer inversion method that adaptively optimizes model complexity. The method quantifies the tool's multi-boundary detection capability using eigenvalue analysis of the Fisher information matrix. Statistical analysis of synthetic models informs the construction of an inversion model library spanning two-to five-layer configurations, facilitating adaptation to diverse formation geometries. To address the dependence of multi-layer inversion on initial values, a progressively increasing model complexity hot-start mechanism is implemented, allowing lower-order inversion results to constrain higher-order models. A comprehensive quality score autonomously selects the optimal inversion model. Numerical examples demonstrate that: (1) in a three-layer sand-shale sequence, the method enhances early recognition of reservoir boundaries due to the model library's coverage of all tool positions; (2) in a six-layer thin-bed model, the trans-layer inversion reduces mean square error by 91.5% compared to conventional three-layer inversion, significantly improves thin-bed imaging resolution, and doubles computational efficiency relative to fixed five-layer inversion; (3) in an anticlinal reservoir model, the method accurately tracks both reservoir structure and internal oil-water contacts; (4) field data validation from a complex clastic reservoir confirms the method's ability to delineate thin shale layers and guide well trajectory in real drilling scenarios. This approach offers a robust solution to the challenges of model applicability and computational efficiency in LWD inversion.