Based on the torque‐axial load coupling properties of twisted cord, a new unipolar composite theory is developed. Overall, the full complement of the so‐called micropolar stress/moment‐strain/rotation gradient coupling is accommodated. This includes the handling of the skew‐symmetric stress to relative matrix wind‐up interaction which is a central feature of continuous twisted cord‐reinforced composites. To establish various interaction effects, both analytical and finite element models of unit cell behavior are employed. Due to the mixed tensor‐vector properties of the constitutive formulation, a specially anisotropic polar formulation is developed. To illustrate the millimeter level importance of polarity, i.e., millipolarity, the results of several case study problems are also presented for cord‐reinforced elastomeric composites. These include both square and alternating (triangular) packing morphologies. To generalize the results, the investigations include a wide range of packing densities.