We present a search for the standard model Higgs boson in 9.5 fb−1 of pp¯ collisions at s=1.96 TeV collected with the D0 detector at the Fermilab Tevatron Collider. The final state considered contains a pair of b jets and is characterized by an imbalance in transverse energy, as expected from pp¯→ZH→νν¯bb¯ production. The search is also sensitive to the WH→ℓνbb¯ channel when the charged lepton is not identified. The data are found to be in good agreement with the expected background. For a Higgs boson mass of 125 GeV, we set a limit at the 95% C.L. on the cross section σ(pp¯→[Z/W]H), assuming standard model branching fractions, that is a factor of 4.3 times larger than the theoretical standard model value, while the expected factor is 3.9. The search is also used to measure a combined WZ and ZZ production cross section that is a factor of 0.94±0.31(stat)±0.34(syst) times the standard model prediction of 4.4 pb, with an observed significance of 2.0 standard deviations.