NASA's OSIRIS-REx and JAXA's Hayabusa2 sample-return missions are currently on their way to encounter primitive near-Earth asteroids (101955) Bennu and (162173) Ryugu, respectively. Spectral and dynamical evidence indicates that these near-Earth asteroids originated in the inner part of the main belt. There are several primitive collisional families in this region, and both these asteroids are most likely to have originated in the Polana-Eulalia family complex. We present the expected spectral characteristics of both targets based on our studies of four primitive collisional families in the inner belt: Polana-Eulalia, Erigone, Sulamitis, and Clarissa. Observations were obtained in the framework of our PRIMitive Asteroids Spectroscopic Survey (PRIMASS). Our results are especially relevant to the planning and interpretation of in situ images and spectra to be obtained by the two spacecraft during the encounters with their targets.