A heterogeneous domain decomposition method is presented for efficiently and effectively analyzing the antenna and radome mounted on a realistic airborne platform. The proposed non-conformal domain decomposition method follows a hierarchical domain partitioning strategy. The entire computational domain is decomposed into non-overlapping sub-regions. A surface integral equation domain decomposition method is applied for the full wave solution of the homogeneous sub-regions, such as airborne platform. A non-conformal finite element domain decomposition method is proposed for solving sub-regions involving significant repetitions: such as large finite antenna arrays, frequency selective surfaces, and metamaterials. To further improve the convergence in the DDM iterations, an optimal 2nd order transmission condition is introduced to enforce field continuities across domain interfaces. A complex airborne antenna system-level simulation is conducted to illustrate the potential benefits offered by the proposed method.