Air mattress on thin groundsheet?

If I were going to put myself in the situation of using a tarp, bivy combo, I would use something like a Gossamer Gear foam. Seems rather light but much more durable.

Here is a link to what I personally would choose:

http://www.gossamergear.com/cgi-bin/gossamergear/thinlight.html
Weight:
1/8" varies: 1.9 – 2.1 oz. (54 – 60 g.)

I've used just a ground sheet and air mattress with no problems. Just check the ground for sharp objects.

It's all about site preparation. Those who are careful and check for spikes have no problems. The POE Ether Elite is fairly robust.

Cheers
PS: watch it in the desert!

Another option similar to G Gear.

http://www.suluk46.com/products%20%20-%20P3%20PG%20Sheet.html

Just go over the area under your tarp with a fine toothed comb and you'll be fine. I've been using a GG polycro ground cloth and a Prolite small with no adverse effects. Actually I'm not sure how beneficial the ground cloth is except for keeping things clean and keeping me from absorbing some moisture from the ground (it collects a lot of condensation on its underside).

+1 with being more careful in the desert. I had to move my entire camp after I set up my Double Rainbow because I realized I was too close to a tree that was dropping pea-sized thorny nubbs.