We are planning to construct a 2-story deck. The floor of the 2nd story will be the ceiling of the 1st story. We want this floor/ceiling to be weatherproof, i.e. no rain penetration. The 2nd story will not be enclosed and will be exposed to rain. Any suggestions on how to construct the 2nd story deck, ensuring adequate drainage with minimum slope and without trapping moisture between the deck material on the 2nd story and the ceiling of the 1st story?

There are very heavy vinyl products which can act as both deck and roof, and there are fiberglass roofs which can also act as a deck. Or one could use tongue-and-groove redwood, like a porch floor. The advantage to the vinyl or fiberglass options is that they are self-flashing. The installer turns up the material at wall junctions, railing posts, etc. to create flashings.

What vinyl products are available, Richard? I'm anxious to do a similar thing with my deck.

http://www.dec-k-ing.com/vinyl.asp

That's for vinyl decking.

This one's for fiberglass:

http://www.fiber-tek.com/sundeck.htm

There are others...google 'fiberglass deck' and you'll find them.