There is a diffusion-open material/plastic that can be used as underlayment instead of solid wood decking and tar paper named Monarperm 900. It is said to be strong, and you can advantageously insulate without an air gap because it is open "on one side."
Information can be found on the manufacturer's website
www.icopal.se -> Products -> Roofs -> Underlayment.
When I Googled, I didn't find exhaustive information, but a few hits on Danish sites about Monarperm 1000 - could it be a successor...?
Is there anyone who knows more about this fantastic material? Monarperm 900 costs approximately 35:-/m2, and it could be worth it when you want to quickly make it tight after erecting roof trusses (upper floor under mansard roof in progress).