We present a multiwavelength study of 28 Galactic massive star-forming H II regions. For 17 of these regions, we present new distance measurements based on Gaia DR2 parallaxes. By fitting a multicomponent dust, blackbody, and power-law continuum model to the 3.6 $mu$m through 10 mm spectral energy distributions, we find that ${sim}34$% of Lyman continuum photons emitted by massive stars are absorbed by dust before contributing to the ionization of H II regions, while ${sim}68$% of the stellar bolometric luminosity is absorbed and reprocessed by dust in the H II regions and surrounding photodissociation regions. The most luminous, infrared-bright regions that fully sample the upper stellar initial mass function (ionizing photon rates $N_C ge 10^{50}~{rm s}^{-1}$ and dust-processed $L_{rm TIR}ge 10^{6.8}$ L$_{odot}$) have on average higher percentages of absorbed Lyman continuum photons ($sim$51%) and reprocessed starlight ($sim$82%) compared to less luminous regions. Luminous H II regions show lower average PAH fractions than less luminous regions, implying that the strong radiation fields from early-type massive stars are efficient at destroying PAH molecules. On average, the monochromatic luminosities at 8, 24, and 70 $mu$m combined carry 94% of the dust-reprocessed $L_{rm TIR}$. $L_{70}$ captures ${sim}52$% of $L_{rm TIR}$, and is therefore the preferred choice to infer the bolometric luminosity of dusty star-forming regions. We calibrate SFRs based on $L_{24}$ and $L_{70}$ against the Lyman continuum photon rates of the massive stars in each region. Standard extragalactic calibrations of monochromatic SFRs based on population synthesis models are generally consistent with our values.