We report a measurement of the time-dependent CP asymmetry of B¯0→DCP(∗)h0 decays, where the light neutral hadron h0 is a π0, η, or ω meson, and the neutral D meson is reconstructed in the CP eigenstates K+K-, KS0π0, or KS0ω. The measurement is performed combining the final data samples collected at the (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)×106BB¯ pairs recorded by the BABAR detector and (772±11)×106BB¯ pairs recorded by the Belle detector. We measure the CP asymmetry parameters -ηfS=+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¯0→DCP(∗)h0 decays. The hypothesis of no mixing-induced CP violation is excluded in these decays at the level of 5.4 standard deviations.