In order to understand slip at the interface between two immiscible polymer liquids in the context of polymer extrusion, we have investigated coaxial two-phase flow using a capillary rheometer. To measure the slip velocity at the polymer/polymer interface we have modified and adapted the Mooney method. Usually, the Mooney method is used to investigate slip at the interface between a polymer and a solid wall. Using the modified Mooney method, we measured the dependence of the interfacial slip velocity on the interfacial shear stress for cylindrical core-sheath samples of two polymer pairs: polypropylene/polystyrene and poly(ethene-co-tetrafluoroethene)/polystyrene. When compared to previous work, we were able to investigate slip over a wider range of shear stress values using the new approach. In agreement with prior work on multilayer sandwiches undergoing drag flow and flow visualization of capillary flow, we found two distinct power-law regimes in the relationship between the interfacial slip velocity and the interfacial shear stress. The power-law exponent at low shear stress values and the critical stress for the transition between the power-law regimes varies with the polymer pair. However, the power-law exponent at high shear stresses appears to be independent of the particular polymer pair. We also investigated the flow conditions under which interfacial roughness was observed. The interfacial roughness increases with interfacial shear stress but only beyond a certain critical stress. Finally, the connection, if any, between interfacial slip and the roughness observed at the polymer/polymer interface will be explored.