  We study the intrinsic geometrical structure of hypersurfaces in 6-manifolds
carrying a balanced Hermitian SU(3)-structure, which we call {\em balanced}
SU(2)-{\em structures}. We provide conditions which imply that such a
5-manifold can be isometrically embedded as a hypersurface in a manifold with a
balanced SU(3)-structure. We show that any 5-dimensional compact nilmanifold
has an invariant balanced SU(2)-structure as well as new examples of balanced
Hermitian SU(3)-metrics constructed from balanced SU(2)-structures. Moreover,
for $n=3,4$, we present examples of compact manifolds, endowed with a balanced
SU(n)-structure, such that the corresponding Bismut connection has holonomy
equal to SU(n).
