  Multi-wavelength observations indicate that some starburst galaxies show a
dominant non-thermal contribution from their central region. These active
galactic nuclei (AGN)-starburst composites are of special interest, as both
phenomena on their own are potential sources of highly-energetic cosmic rays
and associated gamma-ray and neutrino emission. In this work, a homogeneous,
steady-state two-zone multi-messenger model of the non-thermal emission from
the AGN corona as well as the circumnuclear starburst region is developed and
subsequently applied to the case of NGC 1068, which has recently shown some
first indications of high-energy neutrino emission. Here, we show that the
entire spectrum of multi-messenger data - from radio to gamma-rays including
the neutrino constraint - can be described very well if both, starburst and AGN
corona, are taken into account. Using only a single emission region is not
sufficient.
