  We report a measurement of the time-dependent CP asymmetry of B0->D(*)CP h0
decays, where the light neutral hadron h0 is a pi0, eta or omega meson, and the
neutral D meson is reconstructed in the CP eigenstates K+ K-, K0S pi0 or K0S
omega. The measurement is performed combining the final data samples collected
at the Y(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 BB pairs recorded by the BaBar
detector and ( 772 +/- 11 ) x 10^6, BB pairs recorded by the Belle detector. We
measure the CP asymmetry parameters -eta_f S = +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 B0->D(*)CP h0 decays.
The hypothesis of no mixing-induced CP violation is excluded in these decays at
the level of 5.4 standard deviations.
