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,1569s 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 $alpha = -0.53pm0.02$, 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.
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