An amplitude analysis of B0→(π+π−)(K+π−) decays is performed in the two-body invariant mass regions 300<m(π+π−)<1100 MeV/c2, accounting for the ρ0, ω, f0(500), f0(980) and f0(1370) resonances, and 750<m(K+π−)<1200 MeV/c2, 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 ˜f0ρK∗=0.164±0.015±0.022 and ˜f0ωK∗=0.68±0.17±0.16, and their CP asymmetries, A0ρK∗=−0.62±0.09±0.09 and A0ωK∗=−0.13±0.27±0.13, where the first uncertainty is statistical and the second systematic.