This paper presents differential cross-section measurements of events containing a charged lepton, missing transverse momentum, two b-jets, and two light jets, consistent with the W+W−bb¯ final state. The analysis is based on 140 fb−1 of proton-proton collision data at s=13 TeV recorded with the ATLAS detector during Run 2 of the Large Hadron Collider (2015–2018). Differential cross-sections are unfolded at particle level for a range of kinematic observables and in three kinematic regions. Both regions and observables are optimised for sensitivity to the interference between W+W−bb¯ produced with singly and doubly resonant top quarks. Results are compared with various theoretical predictions and deviations are observed in regions sensitive to the interference between singly and doubly resonant top-quark production. The unfolded results provide new information about the modelling of interference and off-shell effects of the W+W−bb¯ final state, improving the understanding of top-quark production mechanisms and providing new inputs for future Monte Carlo generator development.