The Dalitz plot distribution of B0 → D¯ 0Kþπ− decays is studied using a data sample corresponding to 3.0 fb−1 of pp collision data recorded by the LHCb experiment during 2011 and 2012. The data are described by an amplitude model that contains contributions from intermediate Kð892Þ0, Kð1410Þ0, K 2ð1430Þ0 and D 2ð2460Þ− resonances. The model also contains components to describe broad structures, including the K 0ð1430Þ0 and D 0ð2400Þ− resonances, in the Kπ S-wave and the Dπ S- and P-waves. The masses and widths of the D 0ð2400Þ− and D 2ð2460Þ− resonances are measured, as are the complex amplitudes and fit fractions for all components included in the amplitude model. The model obtained will be an integral part of a future determination of the angle γ of the Cabibbo-Kobayashi-Maskawa quark mixing matrix using B0 → DKþπ− decays.