We have obtained spectra of H II regions in the heavily obscured spiral galaxy Maffei 2. The observations have allowed for a determination of the Galactic extinction of this galaxy using a correlation between extinction and hydrogen column density observed among spiral galaxies. The technique reveals that the optical depth of Galactic dust at 1 μm obscuring Maffei 2 is τ₁ = 2.017 ± 0.211, which implies that A_V = 5.58 ± 0.58 mag, significantly higher than observed for the giant elliptical Maffei 1 despite its similar latitude. For comparison, we apply the same technique to IC 342, a neighboring spiral to Maffei 2 but with more moderate obscuration by Galactic dust, owing to its higher Galactic latitude. For this galaxy, we obtain τ₁ = 0.692 ± 0.066, which agrees within errors with the value of 0.639 ± 0.102 derived from the reddening estimate of Schlegel et al. (1998). We therefore adopt the weighted mean of τ₁ = 0.677 ± 0.056 for the extinction of IC 342, which implies that A_V = 1.92 ± 0.16 mag. A new distance estimate for Maffei 2 of 3.34 ± 0.56 Mpc is obtained from a self-consistent Tully-Fisher relation in I adjusted to the NGC 4258 maser zero point. With our new measurement of M_I, Maffei 2 joins Maffei 1 and IC 342 as one of three giant members of the nearby IC 342/Maffei Group of galaxies. We present the revised properties of all three galaxies based on the most accurate extinction and distance estimates to date, accounting for shifts in the effective wavelengths of broadband filters as this effect can be significant for highly reddened galaxies. The revised distances are consistent with what would be suspected for the Hubble Flow, making it highly unlikely that the galaxies interacted with the Local Group since the big bang.