  We explore the model-building and phenomenology of flavored gauge mediation
models of supersymmetry breaking in which the electroweak Higgs doublets and
the SU(2) messenger doublets are connected by a discrete non-Abelian symmetry.
The embedding of the Higgs and messenger fields into representations of this
non-Abelian Higgs-messenger symmetry results in specific relations between the
Standard Model Yukawa couplings and the messenger-matter Yukawa interactions.
Taking the concrete example of an S(3) Higgs-messenger symmetry, we demonstrate
that while the minimal implementation of this scenario suffers from a severe
mu/B_mu problem that is well-known from ordinary gauge mediation, expanding the
Higgs-messenger field content allows for the possibility that mu and B_mu can
be separately tuned, allowing for the possibility of phenomenologically viable
models of the soft supersymmetry breaking terms. We construct toy examples of
this type that are consistent with the observed 125 GeV Higgs boson mass.
