Multilayer mirrors that maintain or increase their reflectivity with increasing incidence angle can be constructed using polymers that exhibit large birefringence in their indices of refraction. The most important feature of these multilayer interference stacks is the index difference in the thickness direction (z axis) relative to the in-plane directions of the film. This z-axis refractive index difference provides a variable that determines the existence and value of the Brewster's angle at layer interfaces, and it controls both the interfacial Fresnel reflection coefficient and the phase relations that determine the optics of multilayer stacks. These films can yield optical results that are difficult or impossible to achieve with conventional multilayer optical designs. The materials and processes necessary to fabricate such films are amenable to large-scale manufacturing.