In this work, chalcogenide all-solid hybrid microstructured optical fibers (Ch-ASHMOF) using As2Se3, As2S5 and AsSe2 glasses are proposed. The polarization-maintaining properties are induced by breaking the symmetry of the rod arrangement and the core shape. The fibers have all-normal chromatic dispersion profiles which are flattened about -10 ps/km/nm over a wavelength range from 5 to 10 m and the birefringence values are up to 4.5x10-4 at 10 μm. By pumping the fiber with a 200-fs-pulse laser source at 5.3 μm, a broad supercontinuum generation from 2 to 10 μm in the mid-infrared window is experimentally demonstrated.