  In the most general two-Higgs-doublet model (2HDM), there is no distinction
between the two complex hypercharge-one SU(2) doublet scalar fields, Phi_a
(a=1,2). Thus, any two orthonormal linear combinations of these two fields can
serve as a basis for the Lagrangian. All physical observables of the model must
therefore be basis-independent. For example, tan(beta)=<Phi_2^0>/<Phi_1^0> is
basis-dependent and thus cannot be a physical parameter of the model. In this
paper, we provide a basis-independent treatment of the Higgs sector with
particular attention to the neutral Higgs boson mass-eigenstates, which
generically are not eigenstates of CP. We then demonstrate that all physical
Higgs couplings are indeed independent of tan(beta). In specialized versions of
the 2HDM, tan(beta) can be promoted to a physical parameter of the
Higgs-fermion interactions. In the most general 2HDM, the Higgs-fermion
couplings can be expressed in terms of a number of physical "tan(beta)--like"
parameters that are manifestly basis-independent. The minimal supersymmetric
extension of the Standard Model provides a simple framework for exhibiting such
effects.
