The Martin-Puplett interferometer (MPI) is a differential Fourier transform spectrometer that measures the difference between spectral brightness at two input ports. This unique feature makes the MPI an optimal zero instrument, able to detect small brightness gradients embedded in a large common background. In this paper, we experimentally investigate the common-mode rejection achievable in the MPI at millimeter wavelengths, and discuss the use of the instrument to measure the spectrum of cosmic microwave background anisotropy.