I think that he is natural born, because of his parentage.
He's natural born because he is entitled to citizenship due to the circumstances of his birth.
Unlike, say Kissinger, Schwarzenegger, or Granholm, each of whom was born foreign (German, Austrian, Canadian, respectively) and each of whom needed to be naturalized in order to acquire US citizenship. Thus, those three are not eligible.
Your son is eligible, as are Cruz, Jindal, Haley, Rubio, McCain, and Obama.
According to the SCOTUS, when determining what the Constitution means, you must give every word purpose, in your understanding of the term natural born Citizen, what purpose do you assign the word ‘natural’? The writers could have simply said “born Citizen”, or “Citizen from birth”. Why the extra word ‘natural’?