A lattice-based self-consistent-field theory is used to reveal the wetting characteristics of a polymeric phase at an interface between two solvent phases. Both solvents are monomeric and the polymer chains are modeled as freely jointed chains of N=100 similar segments. From the polymer point of view we limit our investigations to the symmetric case; both solvents are equally poor for the polymer. We show that the polymer wets the interface both in the limit of strongly and weakly segregated liquids, but that at intermediate values of the L/L demixing the polymer phase can be in a lens configuration (partial wetting). The wetting transitions at strong segregation of the two solvents is always first order, the ones at weak segregation can be either first or second order, depending on the polymer/solvent interactions. For a particular value of the polymer-solvent interaction parameter the two wetting transitions as generated by changing the L/L demixing (then both of the first-order type) merge. At this point the two prewetting lines still exist and obviously merge as well. It is further possible to find detached "prewetting" lines in the regime where the polymer wets the interface at all relevant (i.e., consistent with the presence of three phase coexistence) values of the L/L demixing. Physically this means that there is a range of interfacial widths for which the formation of a new (polymeric) phase is hindered by a free energy barrier at a certain film thickness, but that there is no wetting transition associated with this barrier.