(A) The carriage held but ourselves and immortality: THREE.

(B)The carriage held none but ourselves and immortality:
THREE.

(C) The carriage held but just ourselves and immortality: TWO. Immortality is condition that "I" and "Death" possess.

I can't get the distinction you are making.

I can see the distinction between C and the other two (in A and B immortality is personified and thus a third passenger and in C it is just a trait that they share, like wearing black). It's the difference between A and B that I don't see.