Combining intersection types with higher-order subtyping yields a typed model of object-oriented programming with multiple inheritance [CompagnoniPierce93]. The target calculus, FomegaMeet, a natural generalization of Girard's system Fomega with intersection types and bounded polymorphism, is of independent interest. We prove that subtyping in FomegaMeet is decidable, which yields as a corollary the decidability of subtyping in FomegaSub, its intersection free fragment, because FomegaMeet subtyping system is a conservative extension of that of FomegaSub. Since in both cases subtyping is closed under beta-meet-conversion or beta-conversion of types, which is not the case for the calculus presented in [CastagnaPierce93], solving the problem in the present setting is much more difficult. Moreover, we establish basic structural properties of FomegaMeet and we prove that the type assignment system is sound using a model based on partial equivalence relations.