Households’ allocative decisions have potentially large implications for the health and welfare of their members. We analyze a dataset of rural Bangladeshi households to estimate: (i) a benchmark level of nutritional adequacy that households could afford by selecting different foods and reallocating them among members, and (ii) the associated trade-offs in terms of income and equity preferences. Using a novel set of non-linear health production functions, we show that households can afford adequate diets that meet the clinical needs of nearly all nutrients. Micronutrient adequacy is primarily achieved by changing household-level food choices, while caloric adequacy depends more on intra-household food allocation. We further show that households do not face a clear health-income trade-off. Instead, we find a degree of inequality aversion (for energy) and inequality preference (for micronutrients) that leads to intra-household allocations that are not fully efficient from the perspective of the production of health.