A binned Dalitz plot analysis of the decays B0 → DK∗0, with D → KS0π+π− and D → KS0K+K−, is performed to measure the observables x± and y±, which are related to the CKM angle γ and the hadronic parameters of the decays. The D decay strong phase variation over the Dalitz plot is taken from measurements performed at the CLEO-c experiment, making the analysis independent of the D decay model. With a sample of proton-proton collision data, corresponding to an integrated luminosity of 3.0 fb−1, collected by the LHCb experiment, the values of the CP violation parameters are found to be x+ = 0.05 ± 0.35 ± 0.02, x− = −0.31 ± 0.20 ± 0.04, y+ = −0.81 ± 0.28 ± 0.06 and y− = 0.31 ± 0.21 ± 0.05, where the first uncertainties are statistical and the second systematic. These observables correspond to values γ = (71 ± 20)°, rB0=0.56±0.17 and δB0=(204−20+21)°. The parameters rB0 and δB0 are the magnitude ratio and strong phase difference between the suppressed and favoured B0 decay amplitudes, and have been measured in a region of ±50 MeV/c2 around the K∗(892)0 mass and with the magnitude of the cosine of the K∗(892)0 helicity angle larger than 0.4.