We report the first far-infrared dichroism measurements using a polarization-division interferometer (PDI) developed in our laboratory. This interferometer uses a free-standing wire-grid beamsplitter made of tungsten wires. In conjunction with a linear polarizer in front of the source and two roof-top mirrors (one in each arm of the interferometer), the PDI divides the input beam into two orthogonal linear polarization components, recombines them for interference at the beamsplitter, and directs the output beam at 90 degrees to the direction of the input beam. Light exiting the interferometer is manipulated with far-infrared lenses, to avoid polarization distortions that are inherent to the reflecting surfaces of the mirrors. The performance of the PDI is evaluated by measuring the linear dichroism of oriented PVF2 [poly(vinylidenefluoride) and circular dichroism of alpha-pinene, camphor, and 3-methylcyclohexanone. The dichroic multiplex advantage (ability to measure dichroism in the entire far-infrared region from a single measurement) and throughput advantage are demonstrated. These measurements establish the utility of the PDI in measuring transmission and linear dichroism spectra simultaneously without the need for any additional components. Additional developments appear necessary to establish the circular dichroism measurements when the magnitudes are less than one part in one thousand.