  We discuss the possibility of having a non-minimal scalar sector at the weak
scale within the framework of invisible axion models. To frame our discussion
we consider an extension of the Dine-Fischler-Srednicki-Zhitnitsky invisible
axion model with two additional Higgs doublets blind under the Peccei-Quinn
symmetry. Due to mixing effects among the scalar fields, it is possible to
obtain a rich scalar sector at the weak scale in certain decoupling limits of
the theory. In particular, this framework provides an ultraviolet completion of
the so-called aligned two-Higgs-doublet model and solves the strong CP problem.
The axion properties and the smallness of active neutrino masses are also
discussed.
