Multilayer structures on the basis of n-type (In,Fe)Sb and p-type (Ga,Fe)Sb diluted magnetic semiconductors (DMS) along with separate (In,Fe)Sb and (Ga,Fe)Sb layers were fabricated on GaAs substrates by pulsed laser sputtering of InSb, GaAs, GaSb, Sb and Fe targets in a vacuum. Transmission electron microscopy and energy-dispersive x-ray spectroscopy reveal a strong dependence of the phase composition of the (In,Fe)Sb compound on the growth temperature. An increase of the latter from 220C to 300C leads to a coalescence of Fe atoms and formation of a secondary crystalline phase in the (In,Fe)Sb layer with a total Fe content of ca. 10 at. %. At the same time, the Ga0.8Fe0.2Sb layers obtained at 220C and 300C are single-phase. The separate In0.8Fe0.2Sb and Ga0.8Fe0.2Sb layers grown on i-GaAs at 220C are DMS with Curie temperatures of ca. 190 K and 170 K, respectively. The three-layer p-i-n diode (In,Fe)Sb/GaAs/(Ga,Fe)Sb structure grown on a GaAs substrate at 220C with a Fe content of ca. 10 at. % in the single-phase (In,Fe)Sb and (Ga,Fe)Sb layers has a rather high crystalline quality and can be considered as a prototype of a bipolar spintronic device based on Fe-doped III-V semiconductors.