Double-decker is not an accurate description of most overland trucks, though they do have storage beneath the seats. Camping in tents is typical, and there are only a few operations where you sleep on the truck, sometimes on top of the truck. The weirdest set-up I ever saw was a German bus in West Africa where the passengers slept in little coffin-like cubicles. I tried to find a photo of this to share, but to no avail.
African Trails would not be my pick for an overland company. To begin, the trucks have vinyl windows, which quickly become scratched and foggy. (Not to mention that they are easy to slash, and therefore a security issue.) A truck with glass windows is much preferable.
Given that you are married, and might not want a total party truck, I might look at the more high-end overland companies such as Dragoman, African Travel Company, or Intrepid.
Hope this helps,
BB