  Suppose $G$ is a connected complex Lie group and $H$ is a closed complex
subgroup such that $X := G/H$ is Kaehler and the codimension of the top
non-vanishing homology group of $X$ with coefficients in $\mathbb Z_2$ is less
than or equal to two. We show that $X$ is biholomorphic to a complex
homogeneous manifold constructed using well-known basic building blocks, i.e.,
$\mathbb C, \mathbb C^*$, Cousin groups, and flag manifolds.
