With the growing interest in hollow-core antiresonant fibers (HC-ARF), attributed to the development of their fabrication technology, the appearance of more sophisticated structures is understandable. One of the recently advancing concepts is that of dual hollow-core antiresonant fibers, which have the potential to be used as optical fiber couplers. In the following paper, a design of a dual hollow-core antiresonant fiber (DHC-ARF) acting as a polarization fiber coupler is presented. The structure is based on a highly birefringent hollow-core fiber design, which is proven to be a promising solution for the purpose of propagation of polarized signals. The design of an optimized DHC-ARF with asymmetrical cores is proposed, together with analysis of its essential coupling parameters, such as the extinction ratio, coupling length ratio, and coupling strength. The latter two for the x- and y-polarized signals were ~2 and 1, respectively, while the optical losses were below 0.3 dB/cm in the 1500–1700 nm transmission band.