Dye composition comprising at least one insoluble compound and processes using this composition

Disclosed herein is an aqueous dye composition for dyeing keratin fibers, for example, human keratin fibers such as the hair, comprising, in a suitable dyeing medium: (a) at least one oxidizing agent, (b) at least one water-insoluble oxygenated organic non-dyeing compound, present in an amount of at least 30% by weight relative to the total weight of the dye composition, and (c) at least one oxidation dye precursor and/or at least one direct dye. Also disclosed herein is a process for dyeing human keratin fibers, for example, the hair, comprising applying such a composition to the keratin fibers.