We present a theoretical study of the phase behavior of mixed brushes composed of charged and non-charged polymers that are mutually incompatible. We extend the Edwards formulation for the Green's function to investigation of mixed brushes containing a polyelectrolyte species through the incorporation of the combined electrostatic effects as an additional external field which can be self-consistently computed by a corresponding Poisson-Boltzmann equation. The resultant SCF equations were fully numerically analyzed in planar geometry to achieve results that are exact within the mean field assumption. The surface constrained phase behavior of the mixed brushes (assuming that the brushes are mobile along the interface) was examined using the conventional free energy of mixing analysis. The predictions on the effects of such control variables as the charge content of the polyelectrolyte species, ionic strength of the medium, and the surface grafting density of the chains on the conformation properties and phase behavior of the mixed brushes are presented. The results suggest that an increase in the effective charge on the polyelectrolyte (through variation of either charge content or ionic strength) favors the mixed state, while increasing the grafting density favors phase separation. These results are then expanded to spherical geometry where the effect of curvature on the mixed brush stability is elucidated.