The classical-quantum system heterogeneity (different data characteristics, execution paradigms and synchronization mechanism etc.) renders existing distributed communication mechanisms (e.g. MPI, NCCL etc.) inadequate. This bottleneck severely impairs operational synergy and programming efficiency. Thus, the performance of hybrid applications on classical-quantum heterogeneous infrastructures is directly limited. To address these challenges, this paper proposes a message-passing library tailored for large-scale classical-quantum heterogeneous distributed computing, referred to as MPI-Q. The design centers on three mechanisms. First, it defines a heterogeneous hybrid communication domain that achieves unified management of classical and quantum processes in heterogeneous hybrid systems. Second, it uses a lightweight communication path that allows classical control nodes to send device-ready waveform data directly to quantum MonitorProcesses, avoiding unnecessary relay stages. Third, it establishes a heterogeneous hybrid synchronization mechanism to tackle the problem of timing control for multi-node quantum operations. While retaining the traditional MPI programming model, MPI-Q achieves extension toward quantum subsystems. Experiments on distributed GHZ state preparation demonstrate that this model exhibits near-linear scalability, achieving a maximum speedup of 18.76 times on 24 quantum nodes. This proves that the library can effectively support large-scale heterogeneous hybrid distributed computing applications, filling the technical gap in this field.