  Massive star binaries are critical laboratories for measuring masses and
stellar wind mass-loss rates. A major challenge is inferring viewing
inclination and extracting information about the colliding wind interaction
(CWI) region. Polarimetric variability from electron scattering in the highly
ionized winds provides important diagnostic information about system geometry.
We combine for the first time the well-known generalized treatment of
\citet{brown_polarisation_1978} for variable polarization from binaries with
the semi-analytic solution for the geometry and surface density CWI shock
interface between the winds based on Canto et al 1996. Our calculations include
some simplifications in the form of inverse square-law wind densities and the
assumption of axisymmetry, but in so doing arrive at several robust
conclusions. One is that when the winds are nearly equal (e.g., O\,+\,O
binaries), the polarization has a relatively mild decline with binary
separation. Another is that despite Thomson scattering being a gray opacity,
the continuum polarization can show chromatic effects at ultraviolet
wavelengths but will be mostly constant at longer wavelengths. Finally, when
one wind dominates the other, as for example in WR+OB binaries, the
polarization is expected to be larger at wavelengths where the OB component is
more luminous, and generally smaller at wavelengths where the WR component is
more luminous. This behavior arises because from the perspective of the WR
star, the distortion of the scattering envelope from spherical is a minor
perturbation situated far from the WR star. By contrast, the polarization
contribution from the OB star is dominated by the geometry of the CWI shock.
