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Diboson production ($WW+WZ+ZZ$) has been observed at the Tevatron in hadronic decay modes dominated by the $WW$ process. This paper describes the measurement of the cross section of $WZ$ and $ZZ$ events in final states with large ${\mathrm{E\ensuremath{\llap{\not\;}}}}_{T}$ and using $b$-jet identification as a tool to suppress $WW$ contributions. Because of the limited energy resolution, we cannot distinguish between partially hadronic decays of $WZ$ and $ZZ$, and we measure the sum of these processes. The number of signal events is extracted using a simultaneous fit to the invariant mass distribution of the two jets for events with two $b$-jet candidates and events with fewer than two $b$-jet candidates. We measure a cross section $\ensuremath{\sigma}(p\overline{p}\ensuremath{\rightarrow}WZ,ZZ)={5.8}_{\ensuremath{-}3.0}^{+3.6}\text{ }\text{ }\mathrm{pb}$, in agreement with the standard model.

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