We report a measurement of the time-dependent CP asymmetry of (B) over bar (0) -> D(CP)((*))h(0) decays, where the light neutral hadron h(0) is a pi(0), eta , or omega meson, and the neutral D meson is reconstructed in the CP eigenstates K+K-, K-S(0)pi(0) or K-S(0)omega. The measurement is performed combining the final data samples collected at the Upsilon(4S) resonance by the BABAR and Belle experiments at the asymmetric-energy B factories PEP-II at SLAC and KEKB at KEK, respectively. The data samples contain (471 +/- 3) x 10(6) B (B) over bar pairs recorded by the BABAR detector and (772 +/- 11) x 10(6) B (B) over bar pairs recorded by the Belle detector. We measure the CP asymmetry parameters -eta S-f = +0.66 +/- 0.10(stat) +/- 0.06(syst) and C = -0.02 +/- 0.07(stat) +/- 0.03(syst). These results correspond to the first observation of CP violation in (B) over bar (0) -> D(CP)((*))h(0) decays. The hypothesis of no mixing-induced CP violation is excluded in these decays at the level of 5.4 standard deviations.