We report the elaboration of a hybrid mesophase combining the lamellar order of a lyotropic system of nonionic surfactant and the nematic order of a concentrated solution of inorganic nanorods confined between the surfactant layers. Highly aligned samples of this mesophase can be obtained by thermal annealing, and the orientation of the nanorods is readily controlled with a magnetic field. High-resolution synchrotron X-ray scattering and polarized optical microscopy show that, compared to their isolated counterparts, both the nematic and lamellar orders are altered, demonstrating their interplay.