Non-homogeneous dynamic Bayesian networks (NH-DBNs) are a popular tool for learning networks with time-varying interaction parameters. A multiple changepoint process is used to divide the data into disjoint segments and the network interaction parameters are assumed to be segment-specific. The objective is to infer the network structure along with the segmentation and the segment-specific parameters from the data. The conventional (uncoupled) NH-DBNs do not allow for information exchange among segments, and the interaction parameters have to be learned separately for each segment. More advanced coupled NH-DBN models allow the interaction parameters to vary but enforce them to stay similar over time. As the enforced similarity of the network parameters can have counter-productive effects, we propose a new consensus NH-DBN model that combines features of the uncoupled and the coupled NH-DBN. The new model infers for each individual edge whether its interaction parameter stays similar over time (and should be coupled) or if it changes from segment to segment (and should stay uncoupled).