We have examined in detail the morphologies of seven z~1.5 passively evolving luminous red galaxies using high resolution HST NICMOS and ACS imaging data. Almost all of these galaxies appear to be relaxed systems, with smooth morphologies at both rest-frame UV and visible wavelengths. Previous results from spectral synthesis modeling favor a single burst of star formation more than 1 Gyr before the observed epoch. The prevalence of old stellar populations, however, does not correlate exclusively with early-type morphologies as it does in the local universe; the light profiles for some of these galaxies appear to be dominated by massive exponential disks. This evidence for massive old disks, along with the apparent uniformity of stellar age across the disk, suggests formation by a mechanism better described as a form of monolithic collapse than as a hierarchical merger. These galaxies could not have undergone a single major merging event since the bulk of their stars were formed, more than 1 Gyr earlier. There is at least one case, however, that appears to be undergoing a dry merger, which may be an example of the process that converts these unusual galaxies into the familiar spheroids that dominate galaxies comprising old stellar populations at the present epoch.