Displacement interferometry is widely used for accurately characterizing nanometer and subnanometer displacements in many applications. In many modern systems, fiber delivery is desired to limit optical alignment and remove heat sources from the system, but fiber delivery can exacerbate common interferometric measurement problems, such as periodic nonlinearity, and account for fiber-induced drift. In this Letter, we describe a novel, general Joo-type interferometer that inherently has an optical reference after any fiber delivery that eliminates fiber-induced drift. This interferometer demonstrated no detectable periodic nonlinearity in both free-space and fiber-delivered variants.