countenance vs mien

countenance

noun
  • Appearance, especially the features and expression of the face. 

  • Favour; support; encouragement. 

  • Calm facial expression, composure, self-control. 

verb
  • To tolerate, support, sanction, patronise or approve of something. 

mien

noun
  • A specific facial expression. 

  • Demeanor; facial expression or attitude, especially one which is intended by its bearer. 

How often have the words countenance and mien occurred in a corpus of books? (source: Google Ngram Viewer )