A binned Dalitz plot analysis of the decays B (0) -> DK*(0), with D -> K (S) (0) pi(+)pi(-) and D -> K (S) (0) K+K-, is performed to measure the observables x(+/-) and y(+/-), which are related to the CKM angle gamma 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 gamma = (71 +/- 20)degrees, gamma(B0) = 0.56 +/- 0.17 and delta(B0) = (204(-20)(+21))degrees. The parameters gamma(B0) and delta(B0) are the magnitude ratio and strong phase difference between the suppressed and favoured B-0 decay amplitudes, and have been measured in a region of +/- 50 MeV/c(2) around the K*(892)(0) mass and with the magnitude of the cosine of the K*(892)(0) helicity angle larger than 0.4.