This paper investigates the dispersion relations of longitudinal and transverse waves in a two-dimensional binary complex plasma with a square lattice structure. By deriving the dispersion relations for arbitrary propagation angles, we present a more comprehensive model of lattice dynamics. Our results reveal the influence of particle charge ratio, mass ratio, size and nonlinear charge effects on lattice vibration frequencies, offering novel theoretical insights into wave propagation in complex plasmas. The theoretical predictions are indirectly validated through systematic comparison with previously reported experimental data, providing a generalized approach for analyzing wave behavior in multi-component systems. This study contributes to advancing the understanding of binary complex plasmas and supports the design of stable plasma-based technologies.