  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.
