Mien is a word I don't encounter much, but when I do it always seems like it would have been interchangeable with demeanor. Dictionary definitions don't really clarify much (they still seem interchangeable).
Both seem to refer to someone's outward characteristics (look and behaviour) as a reflection of that person's likely or suspected inner characteristics (mood and temperament).
Are they totally interchangeable, or do they have a subtle difference in meaning or usage? Are there any contexts where you might use one, but the other would be inappropriate?