As of Aperture 3.3 and iPhoto 9.3 the library can be shared between the two programs. So if both iPhoto and Aperture use the same library then the structure will be identical within the limits of the programs themselves.
That is in Aperture the images are in projects but in iPhoto they are in events, so if you look at the library with Aperture you'll see projects with iPhoto you'll see events.
There are some limitations on using the unified Aperture / iPhoto Library:
Aperture books and webpages will not be visible in iPhoto; and images that you have hidden in iPhoto cannot be made visible in Aperture.
Have a look at this KB article: http://support.apple.com/kb/HT5043, i.e. the last section: Notes on working with unified libraries in iPhoto and Aperture
But it says right there:
If you use Faces, Places, have created albums, Smart Albums, or shared photos to Facebook or Flickr, these automatically work across both apps.
I am trying to get the albums I created in Aperture to show up in iPhoto.
In fact my library originally came from iPhoto and many of the albums were created there. But only the Smart Albums are visible, not manual albums.
All my manual albums created in Aperture show in iPhoto. It may be that your Aperture Library needs repairing.
Try the Aperture Library First Aid Tools as described in:
Aperture 3: Troubleshooting Basics: http://support.apple.com/kb/HT3805