The complete solution of a two-phase flow problem requires the solution of appropriate partial differential equations (PDEs) of mass, momentum, and energy in the region occupied by the vapor and in the region occupied by the liquid. The moving interface between each phasic region requires the specification of additional interface conditions. These additional conditions are jump conditions imposed by the mass, momentum, and energy balances at the interface and additional interface ‘constitutive’ equations. These additional interface constitutive equations can also be thought of as internal interface boundary conditions that must be imposed on the PDEs on each side of the interface to secure a well posed problem. It is well known that the characteristic equations in any hyperbolic system give a complete picture of the required boundary conditions or interface shock conditions. In this paper, the limiting form of a set of characteristic equations will be used to determine the nature of the phasic interface conditions that are required in a compressible, viscous, conducting fluid at a mass transfer interface. The analysis will show that the traditional interface modeling constitutive equations are insufficient in number and hence lead to multiple solutions and therefore to an ill-posed problem. The source of the insufficient number of interface conditions will be discussed.