An inflatable cushioning article is made from a multilayer film having a seal layer, a gas barrier layer, and a tie layer adhering the seal layer to the gas barrier layer. The cushioning article has a plurality of inflatable chambers, with each of the chambers having a plurality of cells connected in series to one another via inflation channels. Although the inflatable article can be made from relatively thin films, the article exhibits a relatively high burst pressure and can be inflated to, for example 3 psi, and withstand conditions such as 140 F. and high altitude, without film delamination, seal failure, or film rupture. Preferably, the tie layer comprises an anhydride modified polyolefin having an anhydride content of at least 150 ppm.