The Sgr A-H H ii regions are a collection of sources that may represent one of the most recent sites of star formation in the Galactic center (GC). Examining these H ii regions provides important information on the prevalence and distribution of massive stars in the region and may provide clues on the origin of other massive field stars throughout the GC. In this work, we present infrared imaging observations of the Sgr A-H H ii regions taken with the Faint Object Infrared Camera for the SOFIA Telescope (FORCAST) at 19.7, 25.2, 31.5, and 37.1 m. These data provide high angular resolution maps (∼4″) of the sources, which allow us to study the morphology of spatially extended H ii regions in detail. The wavelength coverage of FORCAST also supplies important constraints on the dust mass, temperature, and luminosity of the sources. We produce spectral energy distribution models using DustEM to measure the luminosity and dust mass, which range from ∼3 × 103 to 6 × 105 L and from ∼6 × 10−4 to 3 × 10−1 M , respectively. Analysis of dust temperatures in the four spatially extended H ii regions (H1, H2, H3, and H5) shows that three of these objects require multiple heating sources, and we identify potential stellar candidates. We also compare the size and morphology of the H ii regions and demonstrate that the properties of H2 are consistent with in situ star formation. Lastly, we identify nine additional sources that may be part of the H complex and provide initial characterizations of their infrared emission.