In this paper, a novel two-dimensional super-resolution angle-of-departure (AoD) and angle-of-arrival (AoA) estimation technique is proposed for wideband millimeter-wave multiple-input multiple-output systems with dual-polarized antenna elements. The key ingredient of the proposed method is the custom designed beam pairs, from which there exists an invertible function of the AoD/AoA. A new multi-layer reference signal structure is developed for the proposed method to facilitate angle estimation for wideband channels with dual-polarized antenna elements. To reduce feedback in closed-loop frequency division duplexing systems, a novel differential feedback strategy is proposed to feedback the estimated angle pairs. Numerical results demonstrate that good azimuth/elevation AoD and AoA estimation performance can be achieved under different levels of signal-to-noise ratio, channel conditions, and antenna array configurations.