In this contribution we determine the eigenmodes propagated along structures consisting of a waveguide embedded in a general multilayered bianisotropic medium. This includes for example microstrips or strip dielectric waveguides on bianisotropic substrates. The analysis presented here is a generalization to bianisotropic layered media of the boundary integral equation technique described in previous publications for isotropic layered media. The set of integral equations is solved by a spectral domain technique. In this spectral technique the layered medium is taken into account by determining the scattering of plane waves in the layered medium. Hence the major part of this publication deals with the scattering of plane waves in a multilayered bianisotropic medium. The described analysis is illustrated with the dispersion curves for thick microstrip lines on various bianisotropic substrates.