Let X be a discrete variety of ℂn. Berenstein and Li [4] obtained a necessary and sufficient analytic condition for X to be interpolating for Ap. In this paper, we extend it to the case when X is a disjoint union of complex affine subspaces of ℂn. As a corollary, we solve an open problem posed by Berenstein and Taylor [8] on the interpolation, when the subvariety under consideration is a disjoint union of complex affine subspaces.