1. An end-to-end quality-of-service (QoS) interoperation apparatus in a heterogeneous network environment, the apparatus comprising: a Next Steps In Signaling (NSIS) Application Programming Interface (NAPI) block for handling an NSIS API at the request of an upper layer; an NSIS entity for handling an NSIS protocol stack at the request of the NAPI block; an Internet Protocol Bearer Service (IP BS) manager for managing an IP BS; a translation block for translating parameters of a 3GPP_CLASS object and a UMTS QoS class in an NSIS message according to a mapping configuration; a memory for storing a software comprising a Universal Mobile Telecommunication System Bearer Service (UMTS BS) manager for managing a UMTS BS; and a processor combined with the memory, for controlling the software.