A method for distributed birefringence measurements is proposed based on the interference pattern generated by the interrogation of a dynamic Brillouin grating (DBG) using two short consecutive optical pulses. Compared to existing DBG interrogation techniques, the method here offers an improved sensitivity to birefringence changes thanks to the interferometric effect generated by the reflections of the two pulses. Experimental results demonstrate the possibility to obtain the longitudinal birefringence profile of a 20 m-long Panda fibre with an accuracy of ~10-8 using 16 averages and 30 cm spatial resolution. The method enables sub-metric and highly-accurate distributed temperature and strain sensing.