With the development of wireless Internet, the interworking of the Third Generation (3G) wide area wireless networks and Wireless Local Area Networks (WLAN) has become a focus of research. 3G systems have their advantages in charging management, roaming, and security facilities, and WLAN systems have the advantages of high bandwidth and low investment cost. Interworking of 3G-WLAN offers characteristics that complement each other perfectly. Several authentication protocols have been proposed to improve security. In this paper, we firstly introduce the architectures of 3G-WLAN interworking and discuss existing problems related to authentication and key agreement procedures. Then, we present two schemes by applying authentication based on EAP-TLS (Extensible Authentication Protocol - Transport Layer Security) and EAP-TTLS (Tunneled TLS) into integrated 3G and WLAN to achieve high end-to-end security and authentication for the users. Finally, we conduct a series of performance evaluation on the energy consumption and latency of standard authentication protocols.