Using the data obtained in the 2012 noise-interferometry experiment in the Straits of Florida, this paper investigates the feasibility of retrieving dispersion curves of acoustic normal modes from two-point noise cross-correlation functions. Simultaneous, continuous records of ambient and shipping noise by two near-bottom hydrophones separated by 5 km in 100 meter-deep water have been cross-correlated to obtain an approximation to the deterministic acoustic Green's function. Dispersion curves of the four lowest-order normal modes have been retrieved from spectrograms of the noise cross-correlation function. The techniquedeveloped in the paper allows one to measure dispersion of individual normal modes to a good accuracy without employing any controlled sound sources or hydrophone arrays. Normal mode dispersion curves provide ample information for solving inverse problems. Our results suggest the possibility of monitoring complex dynamics of the coastal ocean with acoustic daylight by using simple and inexpensive passive acoustic systems.