We study the processes $p\bar{p} \rightarrow WZ \rightarrow \ell\nu\ell^+\ell-$ and $p\bar{p} \rightarrow ZZ \rightarrow \ell^+\ell^-\nu\bar{\nu}, where $\ell$ = $e$ or ${\mu}$. Using 8.6 fb$^{-1} of integrated luminosity collected by the D0 experiment at the Fermilab Tevatron collider, we measure the $WZ$ production cross section to be 4.50$^{+0.63}_{-0.66} pb which is consistent with, but slightly above a prediction of the standard model. The ZZ cross section is measured to be 1.64 $\pm$ 0.46 pb, in agreement with a prediction of the standard model. Combination with an earlier analysis of the $ZZ \rightarrow \ell^+\ell^-\ell^+\ell^-$ channel yields a $ZZ$ cross section of 1.44$^{+0.35}_{-0.34}$ pb.
