  Associated production of the Higgs boson with a top-antitop pair is a key
channel to gather further information on the nature of the newly discovered
boson at the LHC. Experimentally, however, its observation is very challenging
due to the combination of small rates, difficult multi-jet final states and
overwhelming backgrounds. In the Standard Model the largest number of events is
expected when h->bb, giving rise to a WWbbbb signature, deluged in tt+jets. A
promising strategy to improve the sensitivity is to maximally exploit the
theoretical information on the signal and background processes by means of the
matrix element method. We show how, despite the complexity of the final state,
the method can be efficiently applied to discriminate the signal against
combinatorial and tt+jets backgrounds. Remarkably, we find that a moderate
integrated luminosity in the next LHC run will be enough to make the signature
involving both W's decaying leptonically as sensitive as the single-lepton one.
