The relationships between atomic and molecular hydrogen and dust of various sizes in extragalactic star-forming regions are considered, based on observational data from the Spitzer and Herschel infrared space telescopes, the Very Large Array (atomic hydrogen emission) and IRAM (CO emission). The source sample consists of approximately 300 star-forming regions in 11 nearby galaxies. Aperture photometry has been applied to measure the fluxes in eight infrared bands (3.6, 4.5, 5.8, 8, 24, 70, 100, and 160um), the atomic hydrogen 21 cm line, and CO (2-1) line. The parameters of the dust in the starforming regions were determined via synthetic-spectra fitting, such as the total dust mass, the fraction of polycyclic aromatic hydrocarbons (PAHs), etc. Comparison of the observed fluxes with the measured parameters shows that the relationships between atomic hydrogen, molecular hydrogen, and dust are different in low- and high-metallicity regions. Low-metallicity regions contain more atomic gas, but less molecular gas and dust, including PAHs. The mass of dust constitutes about 1% of the mass of molecular gas in all regions considered. Fluxes produced by atomic and molecular gas do not correlate with the parameters of the stellar radiation, whereas the dust fluxes grow with increasing mean intensity of stellar radiation and the fraction of enhanced stellar radiation. The ratio of the fluxes at 8 and 24um, which characterizes the PAH content, decreases with increasing intensity of the stellar radiation, possibly indicating evolutionary variations of the PAH content. The results confirm that the contribution of the 24um emission to the total IR luminosity of extragalactic star-forming regions does not depend on the metallicity.