The Dalitz plot distribution of B0→D¯0K+π− 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 K∗(892)0, K∗(1410)0, K∗2(1430)0 and D∗2(2460)− resonances. The model also contains components to describe broad structures, including the K∗0(1430)0 and D∗0(2400)− resonances, in the Kπ S-wave and the Dπ S- and P-waves. The masses and widths of the D∗0(2400)− and D∗2(2460)− 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→DK+π− decays.