In a peer-to-peer (P2P) overlay network, a large number and various types of peer processes are interconnected in networks and are cooperating by using multimedia contents like movies and music. Here, multimedia contents are in nature distributed to peers in various ways like downloading and caching to the peers. Multimedia streaming is a key technology to realize multimedia applications in networks. In multimedia streaming applications, multimedia contents are required to be reliable and continuously delivered to processes in a real-time manner. Some contents peer may not send packets of a content at a required rate due to limited computation resource and a communication channel may not support enough Quality of Service (QoS) due to congestions and faults. Thus, P2P overlay networks are in nature heterogeneous. In this paper, we newly discuss a heterogeneous asynchronous multi-source streaming (HAMS) model where multiple contents peers transmit packets of a multimedia content to a requesting leaf peer to increase the throughput, reliability, and scalability in P2P overlay networks. Here, some pair of channels between contents and leaf peers may support different QoS. Peers may be faulty and some pair of contents peers may have different transmission rates. Finally, we show the HAMS model can support higher throughput and shorter transmission time than the other models in the evaluation.