An aqueous dispersion containing a vinylidene chloride polymer (P1) containing vinylidene chloride in a proportion of at least 50% by weight, and at least one random, alternating or gradient copolymer (C1) having: a) at least one monomer unit (m1) carrying at least one phosphonate group —PO(OH)(OR1) with R1 being a hydrogen atom or an alkyl radical comprising from 1 to 11 carbon atoms, and b) monomer units (m2) which represent at least 50% by weight of the copolymer (C1), derived from at least one monomer (M2) chosen from styrene, maleic anhydride, itaconic acid and the (meth)acrylic monomers corresponding to the general formula CH2=CR2R3 in which R2 and R3 are described herein, copolymer (C1) not containing monomer units derived from vinylidene chloride.