This is the most commonly used equivalent term in English (adj. "double-deck", i.e. with hyphen).

The Italian text is somewhat lacking.
First of all, the way the term is used is logically incorrect, you add a single (not double) deck to obtain a double deck (Tom's proposal fits in well to correct this, although I prefer deck to floor).

Secondly, in the case of the Carvair, more than a second deck being added to the cockpit, the entire cockpit was basically raised up (I had a model kit of one!) ... the Carvair had an elevated flight deck design that allowed the cargo deck to extend beneath it to the front loading doors (thereby forming a double-deck structure at the forefront of the aircraft)
... see http://en.wikipedia.org/wiki/Aviation_Traders_Carvair

--------------------------------------------------
Note added at 20 hrs (2011-02-22 13:33:55 GMT)
--------------------------------------------------

Sorry, I forgot the hyphens of the example sentence ... should be double-deck and wide-body