Interferometry of ambient and shipping noise in the ocean provides a way to estimate physical parameters of the seafloor and the water column in an environmentally friendly manner without employing any controlled sound sources. With noise interferometry, two-point cross-correlation functions of noise serve as the probing signals and replace the Green's function measured in active acoustic remote sensing. The amount of environmental information that can be obtained with passive remote sensing and the robustness of the estimates of the seafloor parameters increase when contributions of individual normal modes are resolved in the noise cross-correlation function. Using the data obtained in the 2012 noise-interferometry experiment in the Straits of Florida, dispersion curves of the first four normal modes are obtained in this paper by application of the time-warping transform to noise cross correlations. The passively measured dispersion curves are inverted for unknown geoacoustic properties of the seabed. Resulting thickness of the sediment layer and sound speed are consistent with the geoacoustic models obtained earlier by other means.