Coexisting polymer phases are characterized by very small interfacial energies, even well below their critical solution temperature. This situation should readily lead to the exclusion of one of the phases from any interface that favors the other. Such complete wetting behavior from a binary mixture of statistical olefinic copolymers is reported. By means of a self-regulating geometry, it is found that the thickness of a wetting layer of one of the phases at the polymer-air interface, growing from the other coexisting phase, attains macroscopic dimensions, increasing logarithmically with time. These results indicate that binary polymer mixtures could be attractive models for the study of wetting phenomena.