We have developed an analytical theory which describes the equilibrium structure of a polyelectrolyte brush interacting with oppositely charged sublayer. We consider sparsely grafted polyions with quenched charges that are immersed in a salt-free solution and form a brush of thickness H. An oppositely charged sublayer of thickness R is located near the grafting surface. We analyze the cases of partial (H > R) and total (H < R) absorption of polyions into the sublayer. We demonstrate that for partially absorbed polyions (H > R), the brush thickness H is not sensitive to a particular shape and range of charge distribution in sublayer but is determined by the total amount of charge immobilized in sublayer. Our findings indicate that, in a partially absorbed system, the brush undergoes an internal segregation. That is, part of the polyions are totally embedded into the sublayer, while the rest of the chains still form a brush. When the brush is totally absorbed into the sublayer (H < R), the structure of the brush depends on the particular shape of distribution of the immobilized opposite charge.