The present invention relates to a cosmetic composition of water-in-oil emulsion type comprising: —from 8% to 70% by weight of an aqueous phase comprising at least one moisturizer/humectant, —from 30% to 92% by weight relative to the weight of the composition of a lipophilic phase comprising: —1% to 20% by weight relative to the weight of the composition of a polar non-volatile hydrocarbon-based first oil, a volatile or non-volatile, hydrocarbon-based or silicone apolar oil, the composition comprising at least one silicon oil; —a particular solid compound whose melting point is at least 30° C., the composition comprising not more than 20% by weight of the lipophilic phase of hydrocarbon-based apolar compound of synthetic origin, —at least one emulsifying surfactant system. the invention also relates to a lip treatment process in which the composition according to any one of the preceding claims is applied to the lips.