The generalized Higgs mass term NH1N2 of the supersymmetric standard m
odel is used to implement the Peccei-Quinn Symmetry to solve the stron
g-CP problem. Then supersymmetry breaking can generate the Higgs mass
parameter mu of order m(3/2) through soft-breaking parameters. This ki
nd of extension contains extra light fields of the axion supermultiple
t whose dominant coupling may come from the supersymmetric axion-Higgs
-Higgs coupling. We present a working example and discuss the cosmolog
ical implications of the model.