An extension of the self-consistent-held (SCF) lattice theory of polyelectrolyte adsorption, which takes into account electrochemical equilibria at an interface (charge regulation), is presented. The extension consists of replacement of the usual boundary condition of constant surface charge or potential by a charge-potential relation derived from the surface electrochemical equilibria. Most parameters of the model were based on characteristics of real systems, with minimal number of fitting parameters. Theoretical calculations of surface charge density, adsorbed amount, and degree of surface charge compensation by polyelectrolytes as a function of pH and electrolyte concentration were carried out. The results were compared with experimental data. The extended SCF model describes well (at a quantitative level) the surface charge density of the substrate both in the absence and in the presence of adsorbed polyelectrolyte. The theory is also successful in prediction of the main features of the surface charge overcompensation upon polyelectrolyte adsorption under different electrolyte conditions (pH, c(s)). By contrast the adsorbed amount is poorly predicted. We believe that the discrepancies between the experiment and the theory are mostly due to nonequilibrium aspects of the polyelectrolyte adsorption, which are not described by the present equilibrium theory.