In this report, we analyse X-ray induced damage of B₄C-coated bilayer materials under various irradiation geometries, following the conditions of our experiment performed at the free-electron-laser facility SACLA. We start with the discussion of structural damage in solids and damage threshold doses for the experimental system components: B₄C, SiC, Mo and Si. Later, we analyze the irradiation of the experimentally tested coated bilayer systems under two different incidence conditions of a linearly polarized X-ray pulse: (i) grazing incidence, and (ii) normal incidence, in order to compare quantitatively the effect of the pulse incidence on the radiation tolerance of both systems. For that purpose, we propose a simple theoretical model utilizing properties of hard X-ray propagation and absorption in irradiated materials and of the following electron transport. With this model, we overcome the bottleneck problem of large spatial scales, inaccessible for any existing first-principle-based simulation tools due to their computational limitations for large systems. Predictions for damage thresholds obtained with the model agree well with the available experimental data. In particular, they confirm that two coatings tested: 15 nm B₄C/20 nm Mo on silicon wafer and 15 nm B₄C/50 nm SiC on silicon wafer can sustain X-ray irradiation at the fluences up to ~10 μJ/μm2, when exposed to linearly polarized 10 keV X-ray pulse at a grazing incidence angle of 3 mrad. Below we present the corresponding theoretical analysis. Potential applications of our approach for design and radiation tolerance tests of multilayer components within X-ray free-electron-laser optics are indicated.