  We compute the complete set of Higgs-mediated chargino-neutralino two-loop
contributions to the electric dipole moments (EDMs) of the electron and neutron
in the minimal supersymmetric standard model (MSSM). We study the dependence of
these contributions on the parameters that govern CP-violation in the MSSM
gauge-gaugino-Higgs-Higgsino sector. We find that contributions mediated by the
exchange of W H^\pm and Z A^0 pairs, where H^\pm and A^0 are the charged and
CP-odd Higgs scalars, respectively, are comparable to or dominate over those
mediated by the exchange of neutral gauge bosons and CP-even Higgs scalars. We
also emphasize that the result of this complete set of diagrams is essential
for the full quantitative study of a number of phenomenological issues, such as
electric dipole moment searches and their implications for electroweak
baryogenesis.
