  We used the multiplex capabilities of the AAOmega spectrograph at the
Anglo-Australian Telescope to create a half-square-degree map of the neutral
and low-ionized ISM in front of the nearby (~5 kpc), most massive Galactic
globular cluster, omega Centauri. Its redshifted, metal-poor and hot horizontal
branch stars probe the medium-strong Ca II K and Na I D2 line absorption, and
weak absorption in the lambda5780 and lambda5797 Diffuse Interstellar Bands
(DIBs), on scales around a parsec. The kinematical and thermodynamical picture
emerging from these data is that we predominantly probe the warm neutral medium
and weakly-ionized medium of the Galactic Disc-Halo interface, ~0.3-1 kpc above
the mid-plane. A comparison with Spitzer Space Telescope 24-micron and
DIRBE/IRAS maps of the warm and cold dust emission confirms that both Na I and
Ca II trace the overall column density of the warm neutral and weakly-ionized
medium. Clear signatures are seen of the depletion of calcium atoms from the
gas phase into dust grains. Curiously, the coarse DIRBE/IRAS map is a more
reliable representation of the relative reddening between sightlines than the
Na I and Ca II absorption-line measurements, most likely because the latter are
sensitive to fluctuations in the local ionization conditions. The behaviour of
the DIBs is consistent with the lambda5780 band being stronger than the
lambda5797 band in regions where the ultraviolet radiation level is relatively
high, as in the Disc-Halo interface. This region corresponds to a sigma-type
cloud. In all, our maps and simple analytical model calculations show in
unprecedented detail that small-scale density and/or ionization structures
exist in the extra-planar gas of a spiral galaxy. (abridged)
