  We study the resolved radio-continuum spectral energy distribution of the
dwarf irregular galaxy, NGC 1569, on a beam-by-beam basis to isolate and study
its spatially resolved radio emission characteristics. Utilizing high quality
NRAO Karl G. Jansky Very Large Array (VLA) observations that densely sample the
1--34\,GHz frequency range, we adopt a Bayesian fitting procedure, where we use
H$\alpha$ emission that has not been corrected for extinction as a prior, to
produce maps of how the separated thermal emission, non-thermal emission and
non-thermal spectral index vary across NGC\,1569's main disk. We find a higher
thermal fraction at 1\,GHz than is found in spiral galaxies ($26^{+2}_{-3}\%$)
and find an average non-thermal spectral index $\alpha = -0.53\pm0.02$,
suggesting that a young population of cosmic ray electrons is responsible for
the observed non--thermal emission. By comparing our recovered map of the
thermal radio emission with literature H$\alpha$ maps, we estimate the total
reddening along the line of sight to NGC\,1569 to be $E(B-V) = 0.49 \pm 0.05$,
which is in good agreement with other literature measurements. Spatial
variations in the reddening indicate that a significant portion of the total
reddening is due to internal extinction within NGC\,1569.
