To the full order in fermions, we construct D = 10 type II supersymmetric double field theory. We spell the precise N = 2 supersymmetry transformation rules as for 32 supercharges. In terms of a stringy differential geometry beyond Riemann, the constructed action unifies type IIA and IIB supergravities in a manifestly covariant manner with respect to O(10, 10) T-duality and a ‘pair’ of local Lorentz groups, or Spin(1, 9) × Spin(9, 1), besides the usual general covariance of supergravities or the generalized diffeomorphism. The distinction of IIA and IIB may arise after a diagonal gauge fixing of the Lorentz groups. They are identified as two different types of ‘solutions’ rather than two different theories. References: arXiv:1210.5078 (N=2) arXiv:1206.3478 (bosonic N=2) arXiv:1112.0069 (N=1)