A mobile communication device (for example, a cellular telephone) has one air interface for wireless communication with wireless LAN and another air interface for cellular telephone communication with a cellular telephone network. Initially, the communication device is used to transmit VoIP packets of a media stream to a target communication device in a first session across one of the air interfaces. It is then desired to use the other air interface. A spawn SIP message is communicated to the target, which returns a spawn identifier. The communication device sets up a second session by sending a SIP INVITE containing the spawn identifier to the target across the other air interface. Both sessions are active VoIP sessions. The target uses the spawn identifier to associate the first and second sessions. The flow of VoIP packets for the media stream is then switched from the first session to the second session.