We present the results of the combination of searches for the standard model Higgs boson produced in association with a $W$ or $Z$ boson and decaying into $b\overline{b}$ using the data sample collected with the D0 detector in $p\overline{p}$ collisions at $\sqrt{s}=1.96\text{ }\text{ }\mathrm{TeV}$ at the Fermilab Tevatron Collider. We derive 95% C.L. upper limits on the Higgs boson cross section relative to the standard model prediction in the mass range $100\text{ }\text{ }\mathrm{GeV}\ensuremath{\le}{M}_{H}\ensuremath{\le}150\text{ }\text{ }\mathrm{GeV}$, and we exclude Higgs bosons with masses smaller than 102 GeV at the 95% C.L. In the mass range $120\text{ }\text{ }\mathrm{GeV}\ensuremath{\le}{M}_{H}\ensuremath{\le}145\text{ }\text{ }\mathrm{GeV}$, the data exhibit an excess above the background prediction with a global significance of 1.5 standard deviations, consistent with the expectation in the presence of a standard model Higgs boson.