11 pages including authors list (24 in total), 4 figures, 4 tables, submitted to PRD. All figures are available at http://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/PAPERS/TOPQ-2012-16/ - See paper for full list of authorsUsing a sample of dilepton top-quark pair (ttbar) candidate events, a study is performed of the production of top-quark pairs together with heavy-flavor (HF) quarks, ttbar + b + X or ttbar + c + X, collectively referred to as ttbar + HF. The dataset used corresponds to an integrated luminosity of 4.7 fb^-1 of proton--proton collisions at a center-of-mass energy of 7 TeV recorded by the ATLAS detector at the CERN Large Hadron Collider. The dominant background to ttbar + HF in this sample is ttbar + jet events in which a light-f...