  We use the invariance of physical picture under a change of Lagrangian, the
reparametrization invariance in the space of Lagrangians and its particular
case -- the rephrasing invariance, for analysis of the two-Higgs-doublet
extension of the SM. We found that some parameters of theory like tan beta are
reparametrization dependent and therefore cannot be fundamental. We use the
Z2-symmetry of the Lagrangian, which prevents a phi_1 <-> phi_2 transitions,
and the different levels of its violation, soft and hard, to describe a
physical content of the model. In general, the broken Z2-symmetry allows for a
CP violation in the physical Higgs sector. We argue that the 2HDM with a soft
breaking of Z2-symmetry is a natural model in the description of EWSB. To
simplify an analysis we choose among different forms of Lagrangian describing
the same physical reality a specific one, in which the vacuum expectation
values of both Higgs fields are real. A possible CP violation in the Higgs
sector is described by using a two-step procedure with the first step identical
to a diagonalization of mass matrix for CP-even fields in the CP conserved
case. We find very simple necessary and sufficient condition for a CP violation
in the Higgs sector. We determine the range of parameters for which CP
violation and Flavor Changing Neutral Current effects are naturally small,what
corresponds to a small dimensionless mass parameter nu= Re m_{12}^2/(2v1v2). We
discuss how for small nu some Higgs bosons can be heavy, with mass up to about
0.6 TeV, without violating of the unitarity constraints. We discuss main
features of the large nu case, which corresponds for nu -> infty to a
decoupling of heavy Higgs bosons.
