On the basis of first-principles calculations, we report the design of three two-dimensional (2D) binary honeycomb-kagome polymers composed of B- and N-centered heterotriangulenes with a periodically alternate arrangement as in hexagonal boron nitride. The 2D binary polymers with donor-acceptor characteristics are semiconductors with a direct band gap of 1.98-2.28 eV. The enhanced in-plane electron conjugation contributes to high charge carrier mobilities for both electrons and holes, about 6.70 and 0.24 × 103 cm2 V-1 s-1, respectively, for the 2D binary polymer with carbonyl bridges (2D CTPAB). With appropriate band edge alignment to match the water redox potentials and pronounced light adsorption for the ultraviolet and visible range of spectra, 2D CTPAB is predicted to be an effective photocatalyst/photoelectrocatalyst to promote overall water splitting.