  (Abridged)
  Aims: In this paper, we seek to establish the suitability of imaging
spectroscopy performed in the Ca II 854.2 nm line as a means to investigate the
solar chromosphere at high resolution.
  Methods: We utilize monochromatic images obtained with the Interferometric
BIdimensional Spectrometer (IBIS) at multiple wavelengths within the Ca II
854.2 nm line and over several quiet areas. We analyze both the morphological
properties derived from narrow-band monochromatic images and the average
spectral properties of distinct solar features such as network points,
internetwork areas and fibrils.
  Results: The spectral properties derived over quiet-Sun targets are in full
agreement with earlier results obtained with fixed-slit spectrographic
observations, highlighting the reliability of the spectral information obtained
with IBIS. Furthermore, the very narrowband IBIS imaging reveals with much
clarity the dual nature of the Ca II 854.2 nm line: its outer wings gradually
sample the solar photosphere, while the core is a purely chromospheric
indicator. The latter displays a wealth of fine structures including bright
points, akin to the Ca II H2V and K2V grains, as well as fibrils originating
from even the smallest magnetic elements. The fibrils occupy a large fraction
of the observed field of view even in the quiet regions, and clearly outline
atmospheric volumes with different dynamical properties, strongly dependent on
the local magnetic topology. This highlights the fact that 1-D models
stratified along the vertical direction can provide only a very limited
representation of the actual chromospheric physics.
