In Belgium we just finished a traditional double wall log house. Traditional as in: traditional looks, and traditional techniques. We used as the insulation material between the log walls, instead of the more common rock wool or glass wool.
The advantage of is that it absorbs humidity, and can act as a buffer for humidity, just like wood. It breathes, just like wood, and it stores humidity, just like wood. It creates an enormous thermal mass.
The result is a fully damp-open wall, without any membranes or plastic foils. The interior of the wooden house has a very constant humidity and constant temperature thanks to the thermal mass.