  We calculate all gauge invariant Barr-Zee type contributions to fermionic
electric dipole moments (EDMs) in the two-Higgs doublet models (2HDM) with
softly broken Z2 symmetry. We start by studying the tensor structure of h to
VV' part in the Barr-Zee diagrams, and we calculate the effective couplings in
a gauge invariant way by using the pinch technique. Then we calculate all
Barr-Zee diagrams relevant for electron and neutron EDMs. We make bounds on the
parameter space in type-I, type-II, type-X, and type-Y 2HDMs. The electron and
neutron EDMs are complementary to each other in discrimination of the 2HDMs.
Type-II and type-X 2HDMs are strongly constrained by recent ACME experiment's
result, and future experiments of electron and neutron EDMs may search O(10)
TeV physics.
