A measurement of b-hadron pair production is presented, based on a data set corresponding to an integrated luminosity of 11.4 fb−1 of proton-proton collisions recorded at s=8 TeV with the ATLAS detector at the LHC. Events are selected in which a b-hadron is reconstructed in a decay channel containing J/ψ → μμ, and a second b-hadron is reconstructed in a decay channel containing a muon. Results are presented in a fiducial volume defined by kinematic requirements on three muons based on those used in the analysis. The fiducial cross section is measured to be 17.7 ± 0.1(stat.) ± 2.0(syst.) nb. A number of normalised differential cross sections are also measured, and compared to predictions from the Pythia8, Herwig++, MadGraph5_aMC@NLO+Pythia8 and Sherpa event generators, providing new constraints on heavy flavour production.[Figure not available: see fulltext.].