Hmm. She does not seem like any INFJs I know, including you. (and being humanitarian is a requirement in her role of First Lady). I am leaning towards @
Gilly's LSE for her. I considered his LIE for her, but I think for the same reason I do not see her as INFJ, I see her more as S than N. She is more known for her practical projects than her ideas. Her White House veggie garden, and her tweaking regulations to school lunches which are more S than N to me. And N would get to the philosophy/reason behind the menus, while S would make a practical change. She has done the latter. And the ESTJ description fits her. She seems more E than I to me, as her extroverted self is all out there, she shines in the role, and her inner life is smaller.
That would make them semi-duality if he is in fact an ESI. Which makes me the President's Supervisor, and that works for me.
And Semi-Duality makes them a little better relation than super-ego, and it does seem a good one. I do not think he is IEI as @
Tackk suggests. I just don't think he is that much a thinker, and certainly not an ethical type. My Mom is ESI and she was also a good student, co-valedictorian in high school, yet she got there by diligent hard work more than a quick mind, which seems to have been the way Obama achieved as well.
I do not see Barack as EII - he is not ethical enough or intuitive enough and I know my Mirrors, and I do not think Michelle is LSI - she is not intellectually pragmatic enough or Introvert enough.