A rigorous and robust algorithm is presented for solving the electromagnetic scattering problems in the planar multilayered anisotropic and composite media. The Lippman-Schwinger integral formulation is exploited and integrated with the wave iterative technique in the derivation of the spectral-domain state equation. The presented algorithm relies on the accurate expressions of the dyadic Green's function and the introduction of polarization tensor. The Padua-Domínguez interpolation-integration technique is used for improving the computational efficiency. Then, the MUltiple SIgnal Classification (MUSIC) method is utilized for dealing with the inverse imaging problem for the planar multilayered composite structure. The validity of the presented algorithm and the effectiveness of the inverse imaging are verified through numerical examples.