We present an analysis of the molecular hydrogen absorption system at z$_{rm abs}$ = 2.811 in the spectrum of the blazar Q0528-250. We demonstrate that the molecular cloud does not cover the background source completely. The partial coverage reveals
itself as a residual flux in the bottom of saturated H_2 absorption lines. This amounts to about (2.22$pm$0.54)% of the continuum and does not depend on the wavelength. This value is small and it explains why this effect has not been detected in previous studies of this quasar spectrum. However, it is robustly detected and significantly higher than the zero flux level in the bottom of saturated lines of the Ly-alpha forest, (-0.21$pm$0.22)%. The presence of the residual flux could be caused by unresolved quasar multicomponents, by light scattered by dust, and/or by jet-cloud interaction. The H$_2$ absorption system is very well described by a two-component model without inclusion of additional components when we take partial 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$0.02 and 17.82$pm$0.02, respectively. HD molecules are present only in component B. Given the column density, logN(HD)= 13.33$pm$0.02, we find N(HD)/2N(H$_2$)=(1.48$pm$0.10)x10$^{-5}$, significantly lower than previous estimations. We argue that it is crucial to take into account partial coverage effects for any analysis of H$_2$ bearing absorption systems, in particular when studying the physical state of high-redshift interstellar medium.
