Insufficient research has explored whether sociodemographic differences in self-reported, individual-level diet quality are similarly reflected by grocery purchase quality. This cross-sectional analysis of n = 3961 U.S. households from the nationally representative Food Acquisition and Purchase Survey (FoodAPS) compared Healthy Eating Index (HEI)-2015 scores from 1 week of food-at-home acquisitions across self-reported demographic factors (race/ethnicity, Supplemental Nutrition Assistance Program (SNAP) participation, food security, and household-level obesity status). Multivariable-adjusted, survey-weighted regression models compared household HEI-2015 scores across sociodemographic groups. Respondents were primarily White and female, with a mean age of 50.6 years, 14.0% were food insecure, and 12.7% were SNAP-participating. Mean HEI-2015 scores were 54.7; scores differed across all sociodemographic exposures (p < 0.05). Interactions (p < 0.1) were detected between SNAP participation and (1) food insecurity and (2) household-level obesity, and race/ethnicity and (1) household-level obesity. HEI-2015 scores were higher among food secure, non-SNAP households than among food insecure, SNAP-participating households (53.9 ± 0.5 vs. 50.3 ± 0.7, p = 0.007); non-SNAP households without obesity had significantly higher HEI-2015 scores than other households. Household-level obesity was associated with lower HEI-2015 scores in White (50.8 ± 0.5 vs. 52.5 ± 0.7, p = 0.046) and Black (48.8 ± 1.5 vs. 53.1 ± 1.4, p = 0.018) but not Hispanic households (54.4 ± 1.0 vs. 52.2 ± 1.2, p = 0.21). Sociodemographic disparities in household HEI-2015 scores were consistent with previous research on individual-level diet quality.