Underwater visible light communication (UVLC) has been introduced to support emerging high data rate applications such as real-time image and video transmission. Initial works on UVLC build upon the assumption of fixed turbulence strength through the transmission range which can be justified only for horizontal links. In vertical underwater links, the gradient of temperature and salinity changes with depth. This effectively results in ocean stratification where water with different values of salinity and temperature form non-mixing layers. In this paper, we first model the vertical underwater link as a cascaded fading channel where fading coefficients associated with different layers are modeled as independent and non-identical distributed. Based on the cascaded lognormal and Gamma-Gamma distributions respectively for weak and moderate/strong turbulence conditions, we first derive closed-form expressions for the bit error rate (BER) performance of UVLC systems. Then, we analyze the asymptotic BER performance and determine the diversity orders. In addition, we derive closed-form expressions for the average ergodic capacity of underwater cascaded fading channels under consideration. We present simulation results to confirm the analytical findings.