We propose a polarization sensitive terahertz time-domain spectrometer that can record orthogonally polarized terahertz fields simultaneously, using fibre-coupled photoconductive antennas and a scheme that modulated the emitter's polarization. The s and p channels of the multi-pixel terahertz emitter were modulated at different frequencies, thereby allowing orthogonal waveforms to be demultiplexed from the recorded signal in post-processing. The performance of the multi-pixel emitter used in this multiplexing scheme was comparable to that of a commercial single-polarization H-dipole antenna. The approach allowed two orthogonally polarized terahertz pulses to be recorded with good signal to noise (>1000:1) within half a second. We verified the capability of the spectrometer by characterizing a birefringent crystal and by imaging a polarization-sensitive metamaterial. This work has significant potential to improve the speed of terahertz polarization sensitive applications, such as ellipsometry and imaging.