  Let $M$ be a pseudo-Hermitian homogeneous space of finite volume. We show
that $M$ is compact and the identity component $G$ of the group of holomorphic
isometries of $M$ is compact. If $M$ is simply connected, then even the full
group of holomorphic isometries is compact. These results stem from a careful
analysis of the Tits fibration of $M$, which is shown to have a torus as its
fiber. The proof builds on foundational results on the automorphisms groups of
compact almost pseudo-Hermitian homogeneous spaces. It is known that a compact
homogeneous pseudo-K\"ahler manifold splits as a product of a complex torus and
a rational homogeneous variety, according to the Levi decomposition of $G$.
Examples show that compact homogeneous pseudo-Hermitian manifolds in general do
not split in this way.
