In this paper, we investigate the multicarrier transmission in one particular type of underwater acoustic channels, which have extremely long delay spreads (e.g., around 1 s) but clustered multipath arrivals (e.g., two clusters). These channels show up in certain practical scenarios, such as in the deep-water horizontal transmissions and in the underwater broadcasting networks, and introduce both interblock interference and intercarrier interference (IBI/ICI) in the received signal. For joint IBI and ICI mitigation, we propose a factor-graph-based equalization method, in which estimation of information symbols is performed via messages passing over a well-designed graph. We also present a sparse channel estimator by treating the two clusters of the long channel as two virtual quasi-synchronous channels. Both channel estimation and equalization are integrated into a progressive receiver framework. Simulation and experimental results are provided to validate the receiver performance in both deep-water horizontal channels and underwater broadcasting networks.