  This paper extends the nonabelian Hodge correspondence for Kaehler manifolds
to a larger class of hermitian metrics on complex manifolds called balanced of
Hodge-Riemann type. Essentially, it grows out of a few key observations so that
the known results, especially the Donaldson-Uhlenbeck-Yau theorem and
Corlette's theorem, can be applied in our setting. Though not necessarily
Kaehler, we show that the Sampson-Siu Theorem proving that harmonic maps are
pluriharmonic remains valid for a slightly smaller class by using the known
argument. Special important examples include those balanced metrics arising
from multipolarizations.
