We address a problem of fundamental importance in the physics of interfaces, which is central to the description of multiphase fluid dynamics. This work is important to study interfaces in systems such as polymer melts and solutions, where velocity jumps have been observed and interpreted as a manifestation of slip. This is in violation of classical interfacial conditions that require continuity of velocity and has been remedied in the literature via use of ad hoc models, such as the so-called Navier slip condition. This paper suggests that it is possible to obviate completely the need for such an approach. Instead, we show that one simply requires knowledge of the density field and the molar fraction of the fluid components and the dependence of the viscosity on the density. This information can be obtained easily through molecular dynamics simulations.