  We present an analysis of the combined NIRSpec and MIRI spectra of dusty
galaxies between 1.5 - 28 $\mu$m restframe by implementing a differential
extinction model, where the strength of extinction varies across the spectrum
as different layers of the obscuring dust are probed. Our model is able to
recover a 2D distribution of dust temperature and extinction which allows
inference of the physical nature of the dust in these environments. We show
that differential extinction is necessary to reproduce the spectra of 4 highly
obscured Luminous Infrared Galaxies observed with NIRSpec IFU and MIRI MRS,
where simple screen or uniformly mixed dust distributions fail to fit the data.
We additionally compare the extinction of HII regions in these galaxies via
hydrogen recombination lines, the extinction of molecular gas via the H$_2$
lines, Polycyclic Aromatic Hydrocarbons via the 12.7/11.3 PAH ratio and the
stellar continuum. We find that the molecular gas is deeply buried with the HII
regions in star-forming regions, with a similar extinction to the hottest dust
components. However we find the cooler dust to be less obscured, at a similar
extinction to the stellar continuum and PAHs. The nuclei show a complex dust
distribution with VV114 NE, NGC 3256 S, IIZw96 SW showing a deeply buried
continuum source relative to the molecular gas/HII regions. Additionally, NGC
3256 S, NGC 7469 and VV114 SW show an isolated hot dust component, indicative
of AGN heating, where NGC 3256 S and NGC 7469 are previously known AGN.
