Two-dimensional (2D) hybrid perovskites make up an emerging class of materials for optoelectronic applications in which inorganic octahedral layers are separated by nonconductive large organic cations. This leads to a high-dimensional and dielectric confinement and hence a high exciton binding energy, which severely limits their application in devices in which charge carrier separation is required. In this work, we achieve improved charge separation by replacing nonconductive organic cations with organic charge-transfer complexes consisting of a pyrene donor and a tetracyanoquinodimethane acceptor. Steady-state absorption measurements show that these materials exhibit optical features that match with the absorption of the organic charge-transfer complexes. Using microwave conductivity and femtosecond transient absorption, we show that photoexcitation of these charge-transfer states leads to long-lived mobile charges in the inorganic layers. While the efficiency of charge separation is relatively low, these experiments demonstrate that it is possible to induce charge separation in solid-state 2D perovskites by engineering the organic layer.