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We present an analysis of the molecular hydrogen absorption system at z$_{\rmabs}$ = 2.811 in the spectrum of the blazar Q0528-250. We demonstrate that themolecular cloud does not cover the background source completely. The partialcoverage reveals itself as a residual flux in the bottom of saturated H_2absorption lines. This amounts to about (2.22$\pm$0.54)% of the continuum anddoes not depend on the wavelength. This value is small and it explains why thiseffect has not been detected in previous studies of this quasar spectrum.However, it is robustly detected and significantly higher than the zero fluxlevel in the bottom of saturated lines of the Ly-alpha forest,(-0.21$\pm$0.22)%. The presence of the residual flux could be caused byunresolved quasar multicomponents, by light scattered by dust, and/or byjet-cloud interaction. The H$_2$ absorption system is very well described by atwo-component model without inclusion of additional components when we takepartial coverage into account. The derived total column densities in the H$_2$absorption components A and B are logN(H$_2$)[cm$^{-2}$] = 18.10$\pm$0.02 and17.82$\pm$0.02, respectively. HD molecules are present only in component B.Given the column density, logN(HD)= 13.33$\pm$0.02, we findN(HD)/2N(H$_2$)=(1.48$\pm$0.10)x10$^{-5}$, significantly lower than previousestimations. We argue that it is crucial to take into account partial coverageeffects for any analysis of H$_2$ bearing absorption systems, in particularwhen studying the physical state of high-redshift interstellar medium.

Partial covering of emission regions of Q 0528-250 by intervening H$_2$ clouds