A search for heavy pseudoscalar (A) and scalar (H) Higgs bosons decaying into a top quark pair (t (t) over bar) 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 root s = 8 TeV. Interference effects between the signal process and standard model t (t) over bar 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 t (t) over bar 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, tan beta, for m(A/H) > 500 GeV.