Simultaneous measurements of the tt¯, W+W-, and Z/γ∗→ττ production cross-sections using an integrated luminosity of 4.6 fb-1 of pp collisions at √s=7 TeV collected by the ATLAS detector at the LHC are presented. Events are selected with two high transverse momentum leptons consisting of an oppositely charged electron and muon pair. The three processes are separated using the distributions of the missing transverse momentum of events with zero and greater than zero jet multiplicities. Measurements of the fiducial cross-section are presented along with results that quantify for the first time the underlying correlations in the predicted and measured cross-sections due to proton parton distribution functions. These results indicate that the correlated next-to-leading-order predictions for tt¯ and Z/γ∗→ττ underestimate the data, while those at next-to-next-to-leading-order generally describe the data well. The full cross-sections are measured to be σ(tt¯)=181.2±2.8-9.5+9.7±3.3±3.3 pb, σ(W+W-)=53.3±2.7-8.0+7.3±1.0±0.5 pb, and σ(Z/γ∗→ττ)=1174±24-87+72±21±9 pb, where the cited uncertainties are due to statistics, systematic effects, luminosity and the LHC beam energy measurement, respectively. The W+W- measurement includes the small contribution from Higgs boson decays, H→W+W-.