Measurements of the time-dependent CP violation of $\bar{B}^{0} \to D^{(*)} h^{0}$ decays are presented which are sensitive to the angle $\beta$ of the CKM Unitarity Triangle. The measurements make for the first time simultaneous use of the $( 471 \pm 3 )\times 10^6\, B\bar{B}$ pairs collected by the BaBar experiment and the $( 772 \pm 11 )\times 10^6\, B\bar{B}$ pairs collected by the Belle experiment in single physics analyses. We report combined BaBar+Belle results for the time-dependent CP violation of $\bar{B}^{0} \to D^{(*)}_{CP} h^{0}$ decays, where the light neutral hadron $h^{0}$ is a $\pi^{0}$, $\eta$ or $\omega$ meson, and the neutral $D$ meson decays to the two-body CP eigenstates $K^{+}K^{-}$, $K_{S}^{0}\pi^{0}$ or $K_{S}^{0}\omega$. In this first measurement performed on a data sample of more than $1\,\mathrm{ab}^{-1}$, a first observation of CP violation in $\bar{B}^{0} \to D^{(*)}_{CP} h^{0}$ decays governed by mixing-induced CP violation according to $\sin(2\beta)$ is obtained. We measure the CP asymmetry parameters $-\eta_{f}\mathcal{S} = +0.66 \pm 0.10\,(\rm{stat.}) \pm 0.06\,(\rm{syst.})$ and $\mathcal{C} = -0.02 \pm 0.07\,(\rm{stat.}) \pm 0.03\,(\rm{syst.})$. In addition, we report preliminary results of a second ongoing combined BaBar+Belle measurement which will extract the not well-known value of $\cos(2\beta)$ from a time-dependent Dalitz analysis of $\bar{B}^{0} \to D^{(*)} h^{0}$ decays with $D \to K_{S}^{0} \pi^{+} \pi^{-}$ decays.