Two-dimensional metal halide perovskites are highly versatile for light-driven applications due to their exceptional variety in material composition, which can be exploited for the tunability of mechanical and optoelectronic properties. The band-edge emission is defined by the structure and composition of both organic and inorganic layers, and electron-phonon coupling plays a crucial role in the recombination dynamics. However, the nature of the electron-phonon coupling and what kind of phonons are involved are still under debate. Here we investigate the emission, reflectance, and phonon response from single two-dimensional lead iodide microcrystals with angle-resolved polarized spectroscopy. We find an intricate dependence of the emission polarization with the vibrational directionality in the materials, which reveals that several bands of low-frequency phonons with nonorthogonal directionality contribute to the band-edge emission. Such complex electron-phonon coupling requires adequate models to predict the thermal broadening of the emission and provides opportunities to design polarization properties.