It has recently been suggested that stratification of the liquid-vapor interface may be a general structural characteristic of liquids that have a very small ratio of melting temperature to critical temperature, and a pair additive potential that generates a small ratio of melting temperature to critical temperature and a stratified liquid-vapor interface has been developed. In this paper, we examine whether a density independent pair potential that supports a stratified liquid-vapor interface also supports liquid and solid phases with realistic structures and properties. We describe a class of potential energy functions that support "Madrid" liquids, and we report the results of simulations of both the liquid-vapor interface structures and the bulk structures of two such liquids. One of the interesting results obtained is that a "Madrid" potential generates a solid that supports a premelting stage in the melting transition. Since, of simple substances composed of either atomic or very compact molecular species, it is only the liquid-vapor interfaces of metals that are stratified, our analysis addresses whether a density independent potential energy function can simultaneously account for the structures and properties of the liquid-vapor interface and the bulk phases of a metal. We show that even though a Madrid liquid can have a stratified liquid-vapor interface, and thereby resemble a liquid metal, other properties of the Madrid liquid do not agree with the known properties of a liquid metal.