We demonstrate polarization multiplexed dissipative Kerr solitons in an on-chip silicon nitride micro-resonator. In our experiment, TE- and TM-polarized solitons can be individually generated and controlled, thanks to their weak mutual interaction as the result of sufficiently different repetition rates and orthogonal polarization states. Furthermore, we find that TE- and TM-polarized solitons usually exhibit uncorrelated time jitters. Therefore, the frequency and phase coherence between the polarization multiplexed soliton microcombs change dramatically as a function of pump laser parameters, where by optimization, we achieve a narrow dual-microcomb beat note linewidth as small as 4.4 kHz. Potential applications of on-chip polarization multiplexed soliton microcombs include Kerr comb spectral expansion, dual-comb metrology, and measurement of quantum entanglements.