For the first time, the 6-port quadrature and rat-race couplers with balanced-unbalanced-hybrid ports are proposed. The corresponding design methodology is presented, which is capable of designing the proposed couplers with arbitrary power divisions and terminated resistances. In this paper, four types including quadrature and rat-race couplers are fully analyzed, covering all the application configurations of the balanced/unbalanced ports. Besides, the design equations are rigorously derived, with the final design procedures presented. Eventually, prototypes of the four coupler types are fabricated and experimentally measured. The final results sufficiently validate the proposed methodology.