In this work, an analytical study of the electromagnetic propagation in a complex medium-based suspended three-layer coplanar waveguide (CPW) is carried out. The study aims at a numerical calculation of the dominant hybrid mode complex propagation constant in the CPW printed on a bianisotropic substrate. The herein considered bianisotropy is characterized by full 3*3 tensors of permittivity, permeability and magnetoelectric parameters. The study is based on the numerical derivation of the Green's functions of such a complex medium in the spectral domain. The study is carried out using the Full Generalized Exponential Matrix Technique based on matrix-shaped compact mathematical formulations. The Spectral Method of Moments (SMoM) and the Galerkin's procedure are used to solve the resulting homogeneous system of equations. The effect of the chiral and achiral bianisotropy on the complex propagation constant is particularly investigated. Good agreements with available data for an anisotropic-medium-based suspended CPW structure are achieved. Various cases of chiral and achiral bianisotropy have been investigated, and particularly, the effect on the dispersion characteristics is presented and compared with cases of isotropic and bianisotropic Tellegen media.