The microstructure of the binary polymer brushes in the selective solvent was studied using the numerical lattice self-consisting field approach. The case was considered when the selectivity to the solvent (the Flory–Huggins parameter χ) was varied only for one type of chains (responsive chains) while the others (non-responsive chains) remained hydrophilic (χ = 0). In such a brush, with an increase in the hydrophobicity of the responsive chains, a transition occurs between two two-layer microstructures. In the initial state the ends of the longer responsive chains are located near the external surface of the brush and those of non-responsive chains are inside the brush. When the hydrophobicity of the responsive chains becomes high enough then the reversed two-layer microstructure is formed, when the ends of non-responsive chains are located near the brush surface and the responsive chains collapse on the brush bottom. In contrast to previous works, the stiffness parameter (Kuhn segment length p) for one or for both types of chains was varied and its effect on the mechanism and characteristics of the transition was studied. If the stiffness of only responsive chains increases, then the transition occurs with the formation of an intermediate three-layer microstructure, where a layer of responsive chains is located between layers formed by non-responsive ones. If both types of chains have the same p, then the transition occurs gradually without the formation of an intermediate three-layer microstructure. For both cases, the effect of p on the critical value of χ*, corresponding to the transition point and on the steepness of the transition was investigated.