  [Abridged] We present an integrated photometric spectral energy distribution
(SED) of the Magellanic-type galaxy NGC 4449 from the far-ultraviolet (UV) to
the submillimetre, including new observations acquired by the Herschel Space
Observatory. We include integrated UV photometry from the Swift Ultraviolet and
Optical Telescope using a measurement technique which is appropriate for
extended sources with coincidence loss. In this paper, we examine the available
multiwavelength data to infer a range of ages, metallicities and star formation
rates for the underlying stellar populations, as well as the composition and
the total mass of dust in NGC 4449.
  We present an iterative scheme, which allows us to build an in-depth and
multicomponent representation of NGC 4449 `bottom-up', taking advantage of the
broad capabilities of the photoionization and radiative transfer code MOCASSIN
(MOnte CArlo SimulationS of Ionized Nebulae). We fit the observed SED, the
global ionization structure and the emission line intensities, and infer a
recent SFR of 0.4 Msolar/yr and a total stellar mass of approximately 1e9
Msolar emitting with a bolometric luminosity of 5.7e9 Lsolar. Our fits yield a
total dust mass of 2.9e6 Msolar including 2 per cent attributed to polycyclic
aromatic hydrocarbons. We deduce a dust to gas mass ratio of 1/190 within the
modelled region. While we do not consider possible additional contributions
from even colder dust, we note that including the extended HI envelope and the
molecular gas is likely to bring the ratio down to as low as ~ 1/800.
