A weakly charged polyelectrolyte brush in a polar-nonpolar solvent mixture is studied using a boxlike model and by numerical self-consistent-field theory. The work is a continuation of a similar study of a neutral polymer brush in a solvent mixture with a pronounced solubility gap. We study both the structure and structural transitions of the brush in particular in the one-phase region of the solvent mixture in the bulk. With respect to the neutral system, the polyelectrolyte system is even richer in its behavior. Starting from a nonpolar main solvent, upon increasing the chemical potential of water, we find the development of a mesoscopic water film inside the brush. The polymer takes up this thin film as it finds an environment that allows for the dissociation of its groups energetically attractive. The phase transition can be accompanied by an anomalous collapse of the ionizable brush and tuned by the pH of the solution and the ionic strength in the system. Another brush transition can occur when nonpolar solvent is added to a brush immersed in water. Finally, it is feasible that systems exist that feature three successive brush transitions upon changing the bulk composition from pre-binodal, to biphasic, and then to post-binodal compositions, where a forward, a reentry, and again a forward transition are found, respectively.