Two laterally adjacent quantum Hall systems separated by an extended barrier of a thickness on the order of the magnetic length possess a complex Landau band structure in the vicinity of the line junction. The energy dispersion is obtained from an exact quantum-mechanical calculation of the single electron eigenstates for the coupled system by representing the wave functions as a superposition of parabolic cylinder functions. For orbit centers approaching the barrier, the separation of two subsequent Landau levels is reduced from the cyclotron energy to gaps which are much smaller. The position of the anticrossings increases on the scale of the cyclotron energy as the magnetic field is raised. In order to experimentally investigate a particular gap at different field strengths but under constant filling factor, a GaAs/AlGaAs heterostructure with a 52 A thick tunneling barrier and a gate electrode for inducing the two-dimensional electron systems was fabricated by the cleaved edge overgrowth method. The shift of the gaps is observed as a displacement of the conductance peaks on the scale of the filling factor. Besides this effect, which is explained within the picture of Landau level mixing for an ideal barrier, we report on signatures of quantum interferences at imperfections of the barrier which act as tunneling centers. The main features of the recent experiment of Yang, Kang are reproduced and discussed for different gate voltages. Quasiperiodic oscillations, similar to the Aharonov-Bohm effect at the quenched peak, are revealed for low magnetic fields before the onset of the regular conductance peaks.