In a hybrid ac-dc microgrid, stiff voltage sources may appear in either the dc or ac subgrids which gives rise to multiple operation modes as power dispatch changes. This creates a challenge for designing the interlink converter between the ac and dc subgrids since the different modes require different interlink controls. To solve this problem, this paper proposes the concept of a transfverter inspired by how transformers link ac grids. Like a transformer, a transfverter can react to the presence of stiff voltage sources on either the dc or ac side and reflect the “stiffness” and voltage stabilizing capability to the other side. A back-to-back converter with droop control is used as the underlying technology to implement this concept. A novel optimization method called model bank synthesis is proposed to find control parameters for the interlink converter that offer the best controller performance across the different microgrid modes without requiring mode-changing of the controller. The effectiveness of the proposed solution is validated through both simulation and experiments.