The aqueous adhesive composition comprises: - a phenol-aldehyde resin based: - on an aromatic polyaldehyde bearing at least two aldehyde functions, comprising at least one aromatic nucleus, and - on a polyphenol, comprising one or more aromatic nuclei with: in the case of a single aromatic nucleus, the latter bears two or three hydroxyl functions in the meta position in relation to one another, the rest of aromatic nucleus being unsubstituted, in the case of a plurality of aromatic nuclei, at least two thereof each bear two or three hydroxyl functions in the meta position in relation to one another, it being understood that the two positions ortho to at least one of these hydroxyl functions are unsubstituted, - less than 16% by weight of unsaturated diene elastomer latex.