Cosmetic product for modifying the natural colour of keratinous fibres, in particular human hair, comprising (i) at least one package comprising at least one multilayer film comprising at least one first polymer layer, at least one second polymer layer and at least one barrier layer, and (ii) at least one cosmetic composition packaged in the packaging and containing: a) at least one oxidising compound, b) at least one C 8 -C 30 alcohol, c) at least one anionic surfactant selected from compounds of the formula R(OCH 2 CH 2) n -OSO 3 -X +, wherein R represents saturated or unsaturated C 8 -C 30 alkyl radicals, n represents integers from 10 to 50 and X + represents a physiologically acceptable cation, d) at least one non-ionic surfactant and e) at least one thickening agent selected from the group of copolymers of (meth)acrylic acid and (meth)acrylic acid esters, copolymers of (meth)acrylates and (meth)acrylamides, copolymers of hydroxyethyl (meth)acrylates and (meth)acrylamides, copolymers of (meth)acrylates, (meth)acrylamides and ethoxylated (meth)acrylic acid esters and mixtures thereof, in particular copolymers of (meth)acrylic acid and ethyl acrylates, characterised in that the first polymer layer is formed from polyethylene terephthalate or polyethylene naphthalate, in particular polyethylene terephthalate; the second polymer layer is formed from a polyolefin, in particular polyethylene; and the barrier layer is formed from metallised, oriented polypropylene. (i) at least one package comprising at least one multilayer film comprising at least one first polymer layer, at least one second polymer layer and at least one barrier layer, and (ii) at least one cosmetic composition packaged in the packaging and containing: a) at least one oxidising compound, b) at least one C 8 -C 30 alcohol, c) at least one anionic surfactant selected from compounds of the formula R(OCH 2 CH 2) n -OSO 3 -X +, wherein R represents saturated or unsaturated C 8 -C 30 alkyl radicals, n represents integers from 10 to 50 and X + represents a physiologically acceptable cation, d) at least one non-ionic surfactant and e) at least one thickening agent selected from the group of copolymers of (meth)acrylic acid and (meth)acrylic acid esters, copolymers of (meth)acrylates and (meth)acrylamides, copolymers of hydroxyethyl (meth)acrylates and (meth)acrylamides, copolymers of (meth)acrylates, (meth)acrylamides and ethoxylated (meth)acrylic acid esters and mixtures thereof, in particular copolymers of (meth)acrylic acid and ethyl acrylates, a) at least one oxidising compound, b) at least one C 8 -C 30 alcohol, c) at least one anionic surfactant selected from compounds of the formula R(OCH 2 CH 2) n -OSO 3 -X +, wherein R represents saturated or unsaturated C 8 -C 30 alkyl radicals, n represents integers from 10 to 50 and X + represents a physiologically acceptable cation, d) at least one non-ionic surfactant and e) at least one thickening agent selected from the group of copolymers of (meth)acrylic acid and (meth)acrylic acid esters, copolymers of (meth)acrylates and (meth)acrylamides, copolymers of hydroxyethyl (meth)acrylates and (meth)acrylamides, copolymers of (meth)acrylates, (meth)acrylamides and ethoxylated (meth)acrylic acid esters and mixtures thereof, in particular copolymers of (meth)acrylic acid and ethyl acrylates,