The diffusiophoresis of a soft spherical particle normal to two parallel disks subject to an applied ionic concentration gradient is modeled theoretically. The soft particle, which comprises a rigid core and a porous membrane layer, is capable of simulating a wide class of particles such as biocolloids and particles covered by an artificial membrane layer; a rigid particle can also be recovered as the limiting case where the membrane layer is infinitely thin. The problem considered simulates, for example, the chemotaxis of cells or microorganisms. We show that the presence of the membrane layer is capable of yielding complicated diffusiophoretic behavior when the sign of the charge carried by that layer is different from that on the surface of the rigid core of the particle. Both the sign and the magnitude of the diffusiophoretic velocity of a particle can be adjusted through varying the friction coefficient of its membrane layer. These results are of practical significance, for example, in the case where diffusiophoresis is adopted as a separation operation or as a tool to carry and/or control the rate of drug release.