The first measurement of the cross section ratio sigma(t t-bar b b-bar) / sigma(t t-bar jj) is presented using a data sample corresponding to an integrated luminosity of 19.6 inverse femtobarns collected in pp collisions at sqrt(s) = 8 TeV with the CMS detector at the LHC. Events with two leptons (e or mu) and four reconstructed jets, including two identified as b quark jets, in the final state are selected. The ratio is determined for a minimum jet transverse momentum pt of both 20 and 40 GeV. The measured ratio is 0.022 +/- 0.003 (stat) +/- 0.005 (syst) for pt > 20 GeV. The absolute cross sections sigma(t t-bar b b-bar) and sigma(t t-bar jj) are also measured. The measured ratio for pt > 40 GeV is compatible with a theoretical quantum chromodynamics calculation at next-to-leading order.