  A recently proposed scheme for a gauge-invariant treatment of tadpole
corrections in spontaneously broken gauge theories - called Gauge-Invariant
Vacuum expectation value Scheme (GIVS) - is applied to a singlet Higgs
extension of the Standard Model and to the Two-Higgs Doublet Model. In contrast
to previously used tadpole schemes, the GIVS unifies the gauge-invariance
property with perturbative stability. For the Standard Model this was
demonstrated for the conversion between on-shell and MSbar renormalized masses,
where the GIVS leads to very moderate, gauge-independent electroweak
corrections. In models with extended scalar sectors, issues with tadpole
renormalization exist if Higgs mixing angles are renormalized with MSbar
conditions, which is the major subject of this article. In detail, we first
formulate non-linear representations of the extended scalar sectors, which is
an interesting subject in its own right. Then we formulate the GIVS which
employs these non-linear representations in the calculation of the tadpole
renormalization constants, while actual higher-order calculations in the GIVS
proceed in linear representations as usual. Finally, for the considered models
we discuss the next-to-leading-order (electroweak and QCD) corrections to the
decay processes $h/H\to WW/ZZ\to4\,$fermions of the CP-even neutral Higgs
bosons h and H using MSbar-renormalized Higgs mixing angles with the GIVS and
previously used tadpole treatments.
