The invention concerns an adhesive composition useful for providing textile fibres with adhesion to a crosslinkable rubber composition, textile fibres sized with said adhesive composition, a light-permeable composite consisting of said sized textile fibres and a crosslinked rubber composition, and a tyre casing whereof the sidewalls comprise said composite. The inventive adhesive composition comprises an aqueous thermosetting phenolic adhesive including at least a diene elastomer and at least an organic pigment. Said adhesive composition is characterised in that it results from the reaction of said aqueous thermosetting phenolic adhesive and an aqueous pigment dispersion containing said organic pigment.