Transverse transmission concepts in the Fourier transform domain for multilayer planar transmission medium are presented. This complete transverse transmission theory (TIT) is found to be a superset of different Fourier-transform-based numerical techniques widely used in guided wave analysis, namely the modematching method and the spectral-domain approach. The features of the theory are: the expansion of field quantities in longitudinal section (LSE/LSM) modes, the concept of rotation of the transverse field vectors, and a comprehensive algorithm using recursive matrix standard form. It is shown that the mode-matching method and spectral-domain approach are generally equivalent except for the last step of imposing the final boundary conditions, and can therefore be summarized in a unified theory within the framework of TIT. In addition, a new parameter, the polarization coefficient, has been introduced to describe the field polarization of the guided wave in a quantitative manner. It is believed that the present theory will help us to gain more insight into hybrid mode propagation in multilayer planar circuits.