The Dalitz plot distribution of B0→D¯0K+π- decays is studied using a data sample corresponding to 3.0fb-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, K2∗(1430)0 and D2∗(2460)- resonances. The model also contains components to describe broad structures, including the K0∗(1430)0 and D0∗(2400)- resonances, in the Kπ S-wave and the Dπ S- and P-waves. The masses and widths of the D0∗(2400)- and D2∗(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.