We present the design, realization and characterization of strong coupling between an intersubband transition and a monolithic metamaterial nanocavity in the mid-infrared spectral range. We use a ground plane in conjunction with a planar metamaterial resonator for full three-dimensional confinement of the optical mode. This reduces the mode volume by a factor of 1.9 compared to a conventional metamaterial resonator while maintaining the same Rabi frequency. The conductive ground plane is implemented using a highly doped n+ layer which allows us to integrate it monolithically into the device and simplify fabrication.