Thin–film helicoidal bianisotropic mediums (TFHBMs) are rotationally non–homogeneous mediums whose microstructure consists of parallel helical columns. We characterize here the plane–wave response of non–axially excited dielectric TFHBM slabs. The constitutive relations for the dielectric TFHBMs are substituted into the time–harmonic Maxwell curl equations, and a 4 × 4 matrix ordinary differential equation is obtained. The piecewise homogeneity approximation method is shown to be reasonably robust to solve the differential equation. Bragg reflection by non–axially excited dielectric TFHBM slabs is investigated, and transmission characteristics are examined. The effects of several key illumination and constitutive parameters on the response of non–axially excited dielectric TFHBM slabs are studied to elucidate trends in functional relationships. A TFHBM bilayer is presented as an example of a device based on non–axially excited dielectric TFHBMs.