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 con- tributing amplitudes. The CP-averaged longitudinal polarisation fractions of the vector-vector modes are found to be f~0ρK∗ = 0.164 ± 0.015 ± 0.022 and f~0ωK∗ = 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.