We have observed 14 Herbig Ae/Be (HAEBE) sources with the long-baseline near-IR Palomar Testbed Interferometer. All except two sources are resolved at 2.2 μm, with angular sizes generally 5 mas. We determine the size scales and orientations of the 2.2 μm emission using various models: uniform disks, Gaussians, uniform rings, flat accretion disks with inner holes, and flared disks with puffed-up inner rims. Although it is difficult to distinguish different radial distributions, we are able to place firm constraints on the inclinations of most sources; seven objects display significantly inclined morphologies. The inner disk inclinations derived from our near-IR data are generally compatible with the outer disk geometries inferred from millimeter interferometric observations, implying that HAEBE disks are not significantly warped. Using the derived inner disk sizes and inclinations, we compute the spectral energy distributions (SEDs) for two simple physical disk models and compare these with observed SEDs compiled from the literature and new near-IR photometry. While geometrically flat accretion disk models are consistent with the data for the earliest spectral types in our sample (MWC 297, V1685 Cyg, and MWC 1080), the later type sources are explained better through models incorporating puffed-up inner disk walls. The different inner disk geometries may indicate different accretion mechanisms for early- and late-type HAEBE stars.