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 E̸T 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 σ(pp→WZ,ZZ)=5.8+3.6−3.0  pb, in agreement with the standard model.