A variety of multilayer planar transmission lines are analyzed by the generalized spectral-domain immitance approach. The three-directional electromagnetic-held Green's functions excited by horizontal electric currents/fields are analytically derived for a multilayer planar structure. With these explicit field expressions, the planar transmission lines, such as microstrip lines, coplanar waveguides (CPW's) with/without backed conductor, are characterized. Rigorous Poynting vector analysis is utilized to calculate the propagated powers of the fundamental and higher-order modes. According to the propagated power distribution, design considerations for planar transmission lines are discussed. A slightly lossy conductor-backed CPW is proposed to attenuate the unwanted even-mode propagation and to maintain a low loss of the desired CPW odd-mode propagation.