Heterogeneous network, for being characterized as networks accessible using different interfaces, requires application-level protocol abstraction to support seamless mobility among these networks. Session Initiation Protocol (SIP), provides such requirement through application-level signaling which enables establishment, modification, and termination of multimedia session. However, SIP still suffers from minimal handoff delays and packet losses due to its sessionre-establishment process wherein ongoing media transmission is queued until new session is established. This, when real-time application services such as Voice over IP (VoIP) or Multimedia over IP (MoIP) is concerned, is detrimental. In this paper, using Stream Control Transmission Protocol (SCTP), we present a mobility management scheme using SCTP-SIP for real-time services across heterogeneous network which ensures transport-level continuance through the deployment of $It\{multi-homing}$ functionality of SCTP. In our approach, while SIP is used to initiate connection and provide network and location transparency, vertical handoff among heterogeneous network is handled by SCTP, guaranteeing the continuance of media transmission even after handoff. Our approach, when evaluated, guarantees seamless mobility together while satisfying Quality of Service (QoS) requirements for real-time multimedia services. Additionally, our scheme does not involve any changes in underlying network infrastructure, ensuring the ease of deployment.