The coupling between interfacial segregation and structural phase transition is studied in dilute Cu-Ag alloys using Monte Carlo modelling. Both the (0 0 1) surface and the Sigma = 5 (3 1 0) [0 0 1] tilt grain boundary (GB) are considered. The simulations show that the (0 0 I) surface plane undergoes a first order phase transition from a Cu-rich phase to a Ag-rich phase at T = 600 K when varying the bulk concentration within the domain of existence of the Cu(Ag) solid solution. This chemical transition is accompanied by a structural one, the Ag-rich phase having a pseudohexagonal c(10 x 2) structure, in good agreement with experiments. For the GB, two segregation modes are established. For low Ag concentration in bulk, only the GB plane is enriched in Ag and the crystallographic structure of the GB is not modified by the Ag enrichment. At higher bulk concentration, an intergranular wetting is observed: a thin film almost pure in Ag is formed in the region where the GB was initially present. Surprisingly, the Ag film is monocrystalline, indicating that the atomic structure of the GB has disappeared, even if the Cu grains retain their mutual disorientation. The thickness of the Ag film increases when the bulk concentration comes near to the bulk solubility limit. We discuss the possibility of a similar wetting for the (0 0 1) surface and we compare the configurations obtained by equilibrium surface segregation in Cu(Ag) (0 0 1) and by depositing Ag/Cu (0 0 1).