The underwater acoustic channel has been usually modeled as sparse. However, in some scenarios of interest, e.g., shallow water environments due to the interaction with the surface and the seabed, the channel exhibits also a dense arrival of multipath components. In these cases, a Hybrid Sparse/Diffuse (HSD) channel representation, rather than a purely sparse one, may be more appropriate. In this work, we present the HSD channel model and channel estimators based on it. We evaluate these estimation strategies on the SPACE08 experimental data set.We show that the HSD estimators outperform the more conventional purely sparse and least squares estimators. Moreover, we show that an exponential Power Delay Profile (PDP) for the diffuse component is appropriate in scenarios where the receiver is far away from the transmitter. Finally, the HSD estimators and the exponential PDP model are shown to be robust even in scenarios where the channel does not exhibit a diffuse component.