Numerical simulations have been carried out to understand the effects of overlapping cirrus clouds and mineral dust on the high-spectral-resolution infrared spectrum in the 600--2400 cm-1 region. A combination of the discrete ordinates radiative transfer and line-by-line models that account for the multiple scattering and monochromatic molecular absorption in the atmosphere is utilized to simulate the down-looking infrared spectrum at the top of the atmosphere with a resolution of 0.2 cm-1. It is demonstrated that the spectral slope of the infrared radiance in the 800--1000 cm-1 region can be used to discriminate coexisting cirrus-dust scenes from those associated only with cirrus clouds or dust alone. In a case for a cirrus cloud overlapping with a dust layer, the spectral features in the 1100--1200 cm-1 and 1400--1850 cm-1 regions can be potentially useful for retrieving the optical thicknesses of the dust layer and cirrus cloud, respectively.