British invented a tightly woven cotton called Ventile for RAF pilots, which is waterproof, windproof and breathes quite well when not wet.
It has some disadvantages, but it's natural, it doesn't burn and it doesn't make funny noises. There are even some certified organic variants made in Switzerland by Stotz. Many manufacturers in Germany, Scandinavia and UK are adding this to some of their jackets, so it's worth looking around.
Else, Paramo has developed a clever cloth called Analogy, which works in a manner similar to animal fur to push rain out and keep you warm. It's not perfect either, and it's based on synthetic fibers, but it doesn't have nasty plastic coatings. It's used by some mountain guides in my region, and when I asked they were quite satisfied.