An amplitude analysis of ${B^0to (pi^+pi^-) (K^+pi^-)}$ decays is performed in the two-body invariant mass regions ${300 < m(pi^+pi^-)<1100}$ MeV/$c^2$, accounting for the $rho^0$, $omega$, $f_0(500)$, $f_0(980)$ and $f_0(1370)$ resonances, and ${750 < m(K^+pi^-)<1200}$ MeV/$c^2$, which is dominated by the $K^{*}(892)^0$ meson. The analysis uses 3 fb$^{-1}$ of proton-proton collision data collected by the LHCb experiment at centre-of-mass energies of 7 and 8 TeV. The $CP$ averages and asymmetries are measured for the magnitudes and phase differences of the contributing amplitudes. The $CP$-averaged longitudinal polarisation fractions of the vector-vector modes are found to be $tilde{f}^0_{rho K^{*}} = 0.164 pm 0.015 pm 0.022$ and $tilde{f}^0_{omega K^{*}} = 0.68 pm 0.17 pm 0.16$, and their $CP$ asymmetries, $mathcal{A}^0_{rho K^{*}} = -0.62 pm 0.09 pm 0.09$ and $mathcal{A}^0_{omega K^{*}} = -0.13 pm 0.27 pm 0.13$, where the first uncertainty is statistical and the second systematic.
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