Trimethylamine-N-oxide (TMAO) and urea are commonly produced in many extremophilic microorganisms that live in harsh environments. In view of high temperature, high pressure, or high salt content, TMAO is known as a protein structure stabilizer, whereas urea destabilizes protein structures even under ambient conditions. Despite clear evidence, destabilizers are often regarded as chaotropes, meaning water-structure breakers, whereas kosmotropes as water structure makers are classified as stabilizers. Using atomistic molecular dynamics simulations, we study aqueous mixtures of TMAO and urea in various biologically relevant concentrations to gain insight into the molecular details of their mutual cross-interactions and their influence on water dynamics and structure. Our results for binary and ternary solutions in combination with different mixing ratios show that both co-solutes strengthen the water network in terms of dynamic and structural aspects. Slight differences in the water binding behavior between both species result in only negligible compensation effects. The outcomes of our simulations thus question the validity and the ill-considered use of attributes like kosmotropic or chaotropic substances for stabilizers and destabilizers.