  We present an analysis of Higgs-boson production in association with a
top-quark pair at the LHC investigating in particular the final state
consisting of four b jets, two jets, one identified charged lepton and missing
energy. We consider the Standard Model prediction in three scenarios, the
resonant Higgs-boson plus top-quark-pair production, the resonant production of
a top-quark pair in association with a b-jet pair and the full process
including all non-resonant and interference contributions. By comparing these
scenarios we examine the irreducible background for the production rate and
several kinematical distributions. With standard selection criteria the
irreducible background turns out to be three times as large as the signal. For
most observables we find a uniform deviation of eight percent between the
scenario requiring two resonant top quarks and the full process. In particular
phase-space regions the non-resonant contributions cause larger effects, and we
observe shape changes for some distributions. Furthermore we investigate
interference effects and find that neglecting interference contributions
results in an over-estimate of the total cross-section of five percent.
