We study Higgs physics at future e⁺e⁻ colliders taking into account the full set of Feynman diagrams for six fermion final states, which are produced for Higgs masses near or above the two W's threshold. In particular we examine events where one isolated lepton or two isolated leptons of different flavours signal the presence of two W^∗,. For these charged current processes, a detailed analysis of the relevance of irreducible and QCD background shows that appropriate cuts are generally sufficient to deal with it in the case of reconstructed or missing Higgs mass distributions. These latter are however affected by a non-negligible distortion and shift of the maximum.