Measurements are presented of the cross section for the production of at least four jets, of which at least two originate from $b$ quarks, in proton-proton collisions. Data collected with the CMS detector at the LHC at a center-of-mass energy of 7 TeV are used, corresponding to an integrated luminosity of $3\text{ }\text{ }{\mathrm{pb}}^{\ensuremath{-}1}$. The cross section is measured as a function of the jet transverse momentum for ${p}_{\mathrm{T}}>20\text{ }\text{ }\mathrm{GeV}$, and of the jet pseudorapidity for $|\ensuremath{\eta}|<2.4$ ($b$ jets), 4.7 (untagged jets). The correlations in azimuthal angle and ${p}_{\mathrm{T}}$ between the jets are also studied. The inclusive cross section is measured to be $\ensuremath{\sigma}(pp\ensuremath{\rightarrow}2b+2j+X)=69\ifmmode\pm\else\textpm\fi{}3(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}24(\mathrm{syst})\text{ }\text{ }\mathrm{nb}$. The $\ensuremath{\eta}$ and ${p}_{\mathrm{T}}$ distributions of the four jets and the correlations between them are well reproduced by event generators that combine perturbative QCD calculations at next-to-leading-order accuracy with contributions from parton showers and multiparton interactions.