Challenging ground-based optical interferometry projects, such as Stokes parameter imaging, require new techniques and instrumentation. In anticipation of such observations, I progress beyond the mathematics of classical optical interferometry (OIC) to optical interferometric polarimetry (OIP). First, I calculate the behavior of a two-channel coherent-averaging OIP instrument. I then define observables that ease instrumental requirements for counteracting atmospheric effects. In general, the output vectors that arise from these observables can be used only for modeling, but if a priori source information is available, images may be created with a single variable baseline. Next, I derive covariances, signal-to-noise ratios, and biases for the observables and output vectors. I also discuss calibration matrices and demonstrate how they are obtained and applied. Last, I present a simple example of OIP data reduction.