An experimental study of the dynamics of the propagation of 180° domain walls from a first GdFe layer to a second GdFe layer through a very thin TbFe layer is presented. In this system, TbFe constitutes a very hard magnetic layer that acts as an energy barrier. It is shown from relaxation and from quasistatic measurements that the propagation of the domain walls can be analyzed as the crossing of an energy barrier from a metastable state to a stable state. The relaxation data can be fitted with a unique relaxation time, which is quite unusual in magnetism. The system is modeled by an assembly of parallel and similar domain-wall junctions. The evolution of the energy barrier parameters with the thickness of the TbFe layer are reported.