In this work, we analyzed junctions between coaxial waveguides heterogeneously filled with lossy dielectrics. The modal expansion of the electromagnetic fields in a coaxial waveguide with two radial layers is derived in detail, and afterward the formulation is generalized for a multilayer waveguide. The propagation constants for lossy waveguides are determined through the method of winding number, ensuring that all eigenvalues can be found. The mode matching technique is applied in the analysis and design of coaxial structures. The formulation is applied in the optimization of coupling structures and radiating horns with heterogeneous dielectric loading. The heterogeneous filling is used in radiating structures in order to reduce the return loss, and especially to control and improve the shape of the radiation pattern for broadband operation. Additionally, the formulation is used to analyze the electromagnetic propagation in wireless telemetry systems for oil wells.