Topochemical reduction of the double-perovskite oxide Sr2FeIrO6 under dilute hydrogen leads to the formation of Sr2FeIrO4. This phase consists of ordered infinite sheets of apex-linked Fe2+O4 and Ir2+O4 squares stacked with Sr2+ cations and is the first report of Ir2+ in an extended oxide phase. Plane-wave density functional theory calculations indicate high-spin Fe2+ (d(6), S = 2) and low-spin Ir2+ (d(7), S = 1/2) configurations for the metals and confirm that both ions have a doubly occupied d(z2) orbital, a configuration that is emerging as a consistent feature of all layered oxide phases of this type. The stability and double occupation of d(z2) in the Ir2+ ions invites a somewhat unexpected analogy to the extensively studied Ir4+ ion as both ions share a common near-degenerate (d(xy/xz/yz))(5) valence configuration. On cooling below 115 K, Sr2FeIrO4 enters a magnetically ordered state in which the Ir and Fe sublattices adopt type II antiferromagnetically coupled networks which interpenetrate each other, leading to frustration in the nearest-neighbor Fe O Ir couplings, half of which are ferromagnetic and half antiferromagnetic. The spin frustration drives a symmetry-lowering structural distortion in which the four equivalent Ir-O and Fe-O distances of the tetragonal I4/mmm lattice split into two mutually trans pairs in a lattice with monoclinic I112/m symmetry. This strong magneto-lattice coupling arises from the novel local electronic configurations of the Fe2+ and Ir2+ cations and their cation-ordered arrangement in a distorted perovskite lattice.