A promising direction in the development of solid oxide fuel cells (SOFCs) is the reversible approach in which the device operates as fuel cell, producing electricity and heat, and as electrolyzer producing the hydrogen fuel. Reversibility strongly increases the device efficiency. It is very convenient for coupling with Renewable Energy Sources and for off grid applications. Although being very important, this direction of SOFC development still needs serious research efforts for the increase of durability, performances and efficiency and decrease of the switching time. A definitive breakthrough is the separation of the water production/consumption from the two electrodes. This work presents systematic studies on a new design of SOFC with a separate compartment for water formation in fuel cell mode and water injection in electrolyzer mode, named monolithic dual membrane fuel cell. It is based on the discovered property of some proton conducting ceramics to behave as mixed ionic conductors. The first tests of laboratory cells show promising performance with excellent reversibility which opens a pathway for further developments on higher technology readiness level.