We present a multiwavelength study of 28 Galactic massive star-forming HII 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 10mm spectral energy distributions, we find that ~34% of Lyman continuum photons emitted by massive stars are absorbed by dust before contributing to the ionization of HII regions, while ~68% of the stellar bolometric luminosity is absorbed and reprocessed by dust in the HII 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_>=10^50^s^-1^ and dust-processed L_TIR_>=10^6.8^L_{sun}_) have on average higher percentages of absorbed Lyman continuum photons (~51%) and reprocessed starlight (~82%) compared to less luminous regions. Luminous HII regions show lower average polycyclic aromatic hydrocarbon (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_TIR_. L70 captures ~52% of L_TIR_, and is therefore the preferred choice to infer the bolometric luminosity of dusty star-forming regions. We calibrate star formation rates (SFRs) based on L24 and L70 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.