The present invention relates to a composition, preferably a cosmetic composition, in particular for coating keratin fibres such as the eyelashes, comprising:—an aqueous phase,—a lamellar phase Lβ formed by an aqueous phase-structuring surfactant system, said surfactant system comprising a content of surfactant(s) of greater than or equal to 15% by weight relative to the total weight of the composition,—at least one (poly)vinylpyrrolidone hydrophilic polymer present in a content of greater than or equal to 3% by weight of solids relative to the total weight of the composition, the hydrophilic polymer(s) having a weight-average molecular mass Mw ranging from 1500 to 500,000 g/mol. The present invention also relates to a process for coating keratin fibres.
