A search for heavy pseudoscalar (A) and scalar (H) Higgs bosons decaying into a top quark pair (tt[over ¯]) has been performed with 20.3 fb^{-1} of proton-proton collision data collected by the ATLAS experiment at the Large Hadron Collider at a center-of-mass energy sqrt[s]=8 TeV. Interference effects between the signal process and standard model tt[over ¯] production, which are expected to distort the signal shape from a single peak to a peak-dip structure, are taken into account. No significant deviation from the standard model prediction is observed in the tt[over ¯] invariant mass spectrum in final states with an electron or muon, large missing transverse momentum, and at least four jets. The results are interpreted within the context of a type-II two-Higgs-doublet model. Exclusion limits on the signal strength are derived as a function of the mass m_{A/H} and the ratio of the vacuum expectation values of the two Higgs fields, tanβ, for m_{A/H}>500 GeV.