By using the extended boundary condition method, the Debye series is developed for light scattered by a coated nonspherical particle in order to interpret the angular dependence of the scattered intensity in terms of various physical processes. Numerical calculations are performed to study the influence of the coating thickness and the ellipticity of a coated spheroid on the angular position of the alpha and beta primary rainbows, which are produced by partial waves experiencing one internal reflection. The hyperbolic umbilic focal section is demonstrated and is analyzed for both the alpha and the beta rainbows.