  We evaluate the form factors describing the semileptonic decays $\bar{B^0}\to
J/\psi (\eta_c) D^+ \ell^- \bar \nu_\ell$, within the framework of a QCD
relativistic potential model. This decay is complementary to $\bar{B^0}\to
J/\psi (\eta_c) D^+ \pi^-$ in a phase space region where a pion factors out.We
estimate the branching ratio for these semileptonic and nonleptonic channels,
finding $\mathcal{BR}(\bar{B^0} \to J/\psi (\eta_c) D^+ \ell \nu_\ell) \simeq
10^{-13}$, $\mathcal{BR}(\bar{B^0} \to J/\psi D^+ \pi^-) = 3.1 \times 10^{-8}$
and $\mathcal{BR}(\bar{B^0} \to \eta_c D^+ \pi^-) = 3.5 \times 10^{-8}$.
