  The associate production of Higgs bosons with W or Z bosons, known as
Higgs-strahlung, is an important search channel for Higgs bosons at the hadron
colliders Tevatron and LHC for low Higgs-boson masses. We refine a previous
calculation of next-to-leading-order electroweak corrections (and recalculate
the QCD corrections) upon including the leptonic decay of the W/Z bosons,
thereby keeping the fully differential information of the 2-lepton + Higgs
final state. The gauge invariance of the W/Z-resonance treatment is ensured by
the use of the complex-mass scheme. The electroweak corrections, which are at
the level of -(5-10)% for total cross sections, further increase in size with
increasing transverse momenta p_T in differential cross sections. For instance,
for p_T,H >~ 200GeV, which is the interesting range at the LHC, the electroweak
corrections to WH production reach about -14% for M_H = 120GeV. The described
corrections are implemented in the HAWK Monte Carlo program, which was
initially designed for the vector-boson-fusion channel, and are discussed for
various distributions in the production channels pp / p \bar p -> H + l nu_l /
l^-l^+ / nu_l \bar nu_l + X.
