A composition comprising (1) a liquid fatty phase comprising at least one aromatic group-containing oil other than benzene or toluene, (2) a particulate phase, and (3) a thickening agent for the fatty phase, wherein the thickening agent includes at least one polysaccharide ether, and wherein the polysaccharide structure comprises at least two different monosaccharide units, and each unit comprises at least one hydroxyl group etherified by a saturated or unsaturated hydrocarbon chain, and cosmetic use of the composition on the skin and/or lips to limit migration of makeup and care products containing the compositions.