The basic principles for flat roof design apply to a Passivhaus in the same way as any other building, and generally fall into two categories: ventilated roofs or warm roofs.
A ventilated flat roof allows any unwanted interstitial moisture to evaporate away. There should, of course, be less danger of this happening with Passivhaus levels of airtightness as long as the vapour control/airtightness layer is positioned correctly on the warm side of the insulation. TJI timber joists are, again, very useful for giving good structural strength with minimal thermal bridging.
Warm roofs tend to cause less potential interstitial moisture problems by separating the roof structure and placing the rigid insulation on top of the decking.
Another version of the warm roof is the inverted roof. This is where the insulation is placed on top of the roofing membrane to give it protection from sunlight and subsequent differential thermal movement. This places the insulation in a wet position which is not ideal for its thermal integrity, as the thermal performance of all insulation materials is affected by moisture, particularly running water.
The designed U-value can be seriously compromised in flat roofs if there is any potential for moisture in or around insulation material, whether interstitial or from precipitation.
Parapet walls are potentially a very bad thermal bridge if not designed very carefully.