How epithelial cells coordinate their polarity to form complex tissues and organs remains a fundamental question in biology. Here, we characterize a unique type of polarity found in liver tissue - nematic cell polarity, which is different from the common vectorial cell polarity in simple epithelia. We propose a conceptual and algorithmic framework to characterize complex patterns of polarity proteins on the surface of a cell in terms of a multipole expansion. To rigorously quantify previously observed tissue-level patterns of nematic cell polarity (Morales-Navarette et al., bioRxiv:495952, 2018), we introduce the concept of co-orientational order parameters, which generalize the known biaxial order parameters S, P, C, D from the theory of liquid crystals. Applying these concepts to three-dimensional reconstructions of single cells from high-resolution imaging data of mouse liver tissue, we show that the axes of nematic cell polarity of hepatocytes are co-aligned with the biaxially anisotropic sinusoidal network for blood transport. Thus, our study characterizes liver tissue as a biological example of a biaxial liquid crystal. The general methodology developed here could be applied to other tissues or in-vitro organoids.