Spectral observations of asteroid family members provide valuable information regarding parent body interiors, the origin and source regions of near-Earth asteroids, and the link between meteorites and their parent bodies. Asteroids of the Hungaria family represent some of the closest samples to the Earth from a collisional family (∼1.94 AU), permitting observations of smaller family fragments than accessible for Main Belt families. We have carried out a ground-based observational campaign entitled Hungaria Asteroid Region Telescopic Spectral Survey (HARTSS) to record reflectance spectra of these preserved samples from the inner-most regions of the primordial asteroid belt. During HARTSS phase one (Lucas et al. (2017). Icarus 291, 268-287) we found that ∼80% of the background population is comprised of stony S-complex asteroids that exhibit considerable spectral and mineralogical diversity. In HARTSS phase two, we turn our attention to family members to determine if the Hungaria collisional family is compositionally homogeneous or heterogeneous. We use taxonomic classification, geometric albedo (pv) estimates, and near-infrared (NIR) spectral properties to infer the composition of the family. During phase two of HARTSS we acquired NIR spectra of 50 new Hungarias (19 family; 31 background) with the SpeX spectrograph at NASA's Infrared Telescope Facility (IRTF) and with the NICS spectrograph at the Telescopio Nazionale Galileo (TNG). We analyzed X-type spectra for NIR color indices (0.85-J; J-K), and a subtle ∼0.9 μm absorption feature that may be attributed to Fe-poor orthopyroxene ± the sulfide mineral oldhamite. Surviving fragments of an asteroid collisional family typically exhibit similar taxonomies, albedos, and spectral properties. Spectral analysis of Hungaria family X-types and independently calculated WISE albedos for family members (average pv= 0.403; n = 192) is consistent with this scenario. Furthermore, about one-fourth of the background population exhibit similar spectral properties and albedos to family X-types. Spectral observations of 92 Hungaria region asteroids acquired during both phases of HARTSS uncover a compositionally-heterogeneous background population-including two rare olivine-dominated A-types and one apparent D-type interloper-and spectral homogeneity down to ∼2 km for collisional family members. Taxonomy, albedos, and spectral properties indicate that the Hungaria family progenitor was an igneous body that formed under reduced conditions, and was likely consistent in composition with the enstatite achondrite (i.e., aubrite) meteorite group.