Drinking water can contain low levels of micropollutants, as well as disinfection by-products (DBPs) that form from the reaction of disinfectants with organic and inorganic matter in water. Due to the complex mixture of trace chemicals in drinking water, targeted chemical analysis alone is not sufficient for monitoring. The current study aimed to apply in vitro bioassays indicative of adaptive stress responses to monitor the toxicological profiles and the formation of DBPs in three drinking water distribution systems in France. Bioanalysis was complemented with chemical analysis of forty DBPs. All water samples were active in the oxidative stress response assay, but only after considerable sample enrichment. As both micropollutants in source water and DBPs formed during treatment can contribute to the effect, the bioanalytical equivalent concentration (BEQ) approach was applied for the first time to determine the contribution of DBPs, with DBPs found to contribute between 17 and 58% of the oxidative stress response. Further, the BEQ approach was also used to assess the contribution of volatile DBPs to the observed effect, with detected volatile DBPs found to have only a minor contribution as compared to the measured effects of the non-volatile chemicals enriched by solid-phase extraction. The observed effects in the distribution systems were below any level of concern, quantifiable only at high enrichment and not different from bottled mineral water. Integrating bioanalytical tools and the BEQ mixture model for monitoring drinking water quality is an additional assurance that chemical monitoring is not overlooking any unknown chemicals or transformation products and can help to ensure chemically safe drinking water.