The propagation features of electromagnetic waves in 3D photonic crystals (PhC) possessing high dielectric contrast are studied with an account of reflection and refraction of light for the case when the multiple-wave Bragg diffraction regime is of great importance. Comparison of measured and calculated reflectance contours with the energy spectrum of eigenmodes of spatially finite PhC is performed in details. The doublet structure of the Bragg reflectance peaks appeared over some range of incidence angles is shown to be shaped due to the additional eigenmodes which are resonantly excited by diffraction of light on the crystal planes inclined to the lateral ones.