What is the most appropriate English word to describe '面' in phrase like '看在A的面上, B...'
'看在A的面上, B...' is better be translated as " Out of respect to A, B..."
  
  Example: "看在你妈妈的面上，我就不为难你" - " Out of respect to your mother, I'll let you off the hook'


~


  As for '看在A的份上, B...', I would translate it as 
  
  "For A's sake, B..." 
  
  or 
  
  "With consideration for A, B..."
  
  Examples: 
  
  "看在你妈妈的份上，我就不为难你" - "For your mother's sake, I'll let you off the hook" 
  
  or 
  
  "看在你妈妈的份上，我就不为难你" - "With consideration for your mother, I'll let you off the hook"