The cross sections for the production of $t\bar{t}b\bar{b}$ and ${t\bar{t}jj}$ and their ratio $\sigma_{t\bar{t}b\bar{b}}/\sigma_{t\bar{t}jj}$ are measured using data corresponding to an integrated luminosity of 2.3 fb$^{-1}$ collected in pp collisions at $\sqrt{s}$=13 TeV with the CMS detector at the LHC. Events with two leptons (e or $\mu$) and at least four reconstructed jets, including at least two identified as b quark jets, in the final state are selected. In the full phase space, the measured ratio is 0.022 $\pm$ 0.003 (stat) $\pm$ 0.006 (syst), the cross section $\sigma_{t\bar{t}b\bar{b}}$ is 4.0 $\pm$ 0.6 (stat) $\pm$ 1.3 (syst) pb and $\sigma_{t\bar{t}jj}$ is 184 $\pm$ 6 (stat) $\pm$ 33 (syst) pb . The measurements are compared with the standard model expectations obtained from a powheg simulation at next-to-leading-order interfaced with pythia.