A hybrid mode analysis is presented for a multilayer dielectric within a rectangular conducting box. An arbitrary set of planar conductors may be distributed along one of the surfaces. The problem is formulated in terms of a rigorous hybrid-mode representation, superposition of TE and TM fields. The analysis combines a transfer-matrix approach with Galerkin´s method in the spectral domain to give a characteristic equation for the dispersion properties of the lines. Among the advantages of the method are its simplicity and rapid convergence, allowing a characterization of the fundamental and higher order modes. Theoretical and practical results are presented, for single/coupled lines and linear resonators, and they are compared with the results presented by other authors. The effects due to metallization, loss and discontinuities are also considered.