The paper presents the results of theoretical justification of the appearance of combinational pulses in the time responses of coupled transmission lines with inhomogeneous dielectric filling. Combinational pulses are of interest because their arrival times do not correspond to the per-unit-length delays of the modes propagating in the lines, but consist of their combinations. They appear because of the asymmetry of the line cross section or boundary conditions. In this study, we formulated analytical expressions for calculating time responses that include combinational pulses, which extends the theory of transmission lines and the development of protection devices based on modal decomposition of pulses. Additionally, we optimized asymmetric structures according to amplitude and time criteria and considering combinational pulses to increase the attenuation of interfering UWB-pulses. We also designed layouts of asymmetric transmission lines with broad-side and edge couplings and investigated them experimentally. The time responses obtained by electrodynamic simulations and measurements confirm the appearance of combinational pulses, which has previously been shown only by quasi-static lossless simulations.