In the past few years, several disks with inner holes that are empty of small dust grains have been detected and are known as transitional disks. Recently, Spitzer has identified a new class of pre-transitional disks with gaps; these objects have an optically thick inner disk separated from an optically thick outer disk by an optically thin disk gap. A near-infrared spectrum provided the first confirmation of a gap in the pre-transitional disk of LkCa 15 by verifying that the near-infrared excess emission in this object was due to an optically thick inner disk. Here we investigate the difference between the nature of the inner regions of transitional and pre-transitional disks using the same veiling-based technique to extract the near-infrared excess emission above the stellar photosphere. We show that the near-infrared excess emission of the previously identified pre-transitional disks of LkCa 15 and UX Tau A in Taurus as well as the newly identified pre-transitional disk of ROX 44 in Ophiuchus can be fit with an inner disk wall located at the dust destruction radius. We also model the broad-band SEDs of these objects, taking into account the effect of shadowing by the inner disk on the outer disk, considering the finite size of the star. The near-infrared excess continua of these three pre-transitional disks, which can be explained by optically thick inner disks, are significantly different from that of the transitional disks of GM Aur, whose near-infrared excess continuum can be reproduced by emission from sub-micron-sized optically thin dust, and DM Tau, whose near-infrared spectrum is consistent with a disk hole that is relatively free of small dust. The structure of pre-transitional disks may be a sign of young planets forming in these disks and future studies of pre-transitional disks will provide constraints to aid in theoretical modeling of planet formation.