Over the years a password has been used as a popular authentication method between a client and a server because of its easy-to-memorize property. But, most password-based authentication services have focused on a same password authentication scheme which provides an authentication and key exchange between a client and a server with the same password. With rapid change of communication environments in the fields such as mobile networks, home networking, etc., the end-to-end security allowing users to hold different password is considered as one of main concerns. In this paper, we consider a new authentication service of how each client with different own password is able to authenticate each other, which is a quite new service paradigm among the existing services. This new service can be used in the current or next generation network environment where a mobile user in cell A wants to establish a secure end-to-end channel with users in ceil B, C, and D using only their memorable passwords. This end-to-end security service minimizes the interferences from the operator controlled by network components. To achieve this end-to-end security, we propose an authentication and key exchange service for group users in different realm, and analyze its security in a formal way. We also discuss a generic construction with the existing authentication schemes.