Objective: To examine the effects of health-related food taxes on substitution and complementary purchases within food groups, including from unhealthier to healthier alternatives and between brands. Methods: We used data from a virtual supermarket experiment with data from 4,259 shopping events linked to varying price sets. Substitution or complementary effects within six frequently purchased food categories were analyzed. Products’ own- and cross-price elasticities were analyzed using Almost Ideal Demand System models. Results: Overall, 37.5% of cross-price elasticities were significant (p < 0.05) and included values greater than 0.10. Supplementary and complementary effects were particularly found in the dairy, meats and snacks categories. For example, a 1% increase in the price of high saturated fat dairy was associated with a 0.18% (SE 0.06%) increase in purchases of low saturated fat dairy. For name- and home-brand products, significant substitution effects were found in 50% (n = 3) of cases, but only in one case this was above the 0.10 threshold. Conclusions/policy implications: Given the relatively low own-price elasticities and the limited substitution and complementary effects, relatively high taxes are needed to substantively increase healthy food purchases at the population level. Trial registration: This study included secondary analyses; the original trial was registered in the Australian New Zealand Clinical Trials Registry ACTRN12616000122459.