The present disclosure relates to a dye composition comprising at least one dye, at least one nonionic surfactant, at least one cationic associative polymer, at least one fatty alcohol and at least one fatty acid ester, wherein the fatty alcohol/nonionic surfactant weight ratio is greater than 0.5 and water is present in the dye composition in an amount greater than or equal to 55% by weight. The disclosure also relates to a process for dyeing keratin fibers using such a composition, and also to a multi-compartment device or kit separately containing the dye composition and an oxidizing composition.