A hybrid cryptosystem combines two systems that fulfill the same cryptographic functionality, and its security enjoys the security of the harder one. There are many proposals for hybrid public-key encryption (hybrid PKE), hybrid signature (hybrid SIG) and hybrid authenticated key exchange (hybrid AKE). In this paper, we fill the blank of Hybrid Password Authentication Key Exchange (hybrid PAKE).     For constructing hybrid PAKE, we first define an important class of PAKE – full DH-type PAKE, from which we abstract sufficient properties to achieve UC security. Our full DH-type PAKE framework unifies lots of PAKE schemes like SPAKE2, TBPEKE, (Crs)X-GA-PAKE, and summarizes their common features for UC security.     Stepping from full DH-type PAKE, we propose two generic approaches to hybrid PAKE, parallel composition and serial composition. Our generic constructions of hybrid PAKE result in a variety of hybrid PAKE schemes enjoying different nice features, like round-optimal, high efficiency, or UC security in quantum random oracle model (QROM).