Noncovalent bonding between atmospheric molecules is central to the formation of aerosol particles and cloud condensation nuclei and, consequently, radiative forcing. While our understanding of O-H⋯B interactions is well developed, S-H⋯B hydrogen bonding has received far less attention. Sulfur- and nitrogen-containing molecules, particularly amines, play a significant role in atmospheric chemistry, yet S-H⋯N interactions are not well understood at a fundamental level. To help characterize these systems, H2S and methyl-, ethyl-, n-propyl-, dimethyl-, and trimethylamine (MA, EA, n-PA, DMA, and TMA) have been investigated using matrix isolation Fourier transform infrared spectroscopy and high-level theoretical methods. Experiments showed that H2S forms hydrogen bonded complexes with each of the amines, with bond strengths following the trend MA ≈ EA ≈ n-PA < TMA ≤ DMA, in line with past experimental work on H2SO4·amine complexes. However, the calculated results indicated that the trend should be MA < DMA < TMA, in line with past theoretical work on H2SO4·amine complexes. Evidence of strong Fermi resonances indicated that anharmonicity may play a critical role in the stabilization of each complex. The theoretical results were able to replicate experiment only after binding energies were recalculated to include the anharmonic effects. In the case of H2SO4·amine complexes, our results suggest that the discrepancy between theory and experiment could be reconciled, given an appropriate treatment of anharmonicity.