Deflatable inflatable web

A protective packaging web, comprising:

• a flexible inflatable web that includes inflatable chambers having inlets and configured for receiving a fluid from the inlets and sealing the fluid therein, the inflatable chambers being configured such that, when inflated, the inflatable web structure has a first contoured exterior surface including a plurality of peaks and valleys, with the peaks defining a phantom first tangential surface connecting the plurality of peaks, the inlets further being configured to allow fluid to flow out from the inflatable chambers;
• and
• a flexible first outer ply affixed to the peaks and detached from the valleys of the first contoured surface, such that when the inflatable chambers are inflated, the first outer ply extends along the phantom first tangential surface, bridging the valleys of the first contoured surface, such that when the chambers are inflated the affixed first outer ply and the inflatable web cooperatively form a framed structure having significantly elevated bending stiffness compared to a bending stiffness resulting from the inflatable web structure absent the attached first outer ply.