This paper introduces Genesis, the first compiler designed to supportHamiltonian Simulation on hybrid continuous-variable (CV) and discrete-variable(DV) quantum computing systems. Genesis is a two-level compilation system. Atthe first level, it decomposes an input Hamiltonian into basis gates using thenative instruction set of the target hybrid CV-DV quantum computer. At thesecond level, it tackles the mapping and routing of qumodes/qubits to implementlong-range interactions for the gates decomposed from the first level. Ratherthan a typical implementation that relies on SWAP primitives similar toqubit-based (or DV-only) systems, we propose an integrated design ofconnectivity-aware gate synthesis and beamsplitter SWAP insertion tailored forhybrid CV-DV systems. We also introduce an OpenQASM-like domain-specificlanguage (DSL) named CVDV-QASM to represent Hamiltonian in terms ofPauli-exponentials and basic gate sequences from the hybrid CV-DV gate set.Genesis has successfully compiled several important Hamiltonians, including theBose-Hubbard model, $\mathbb{Z}_2-$Higgs model, Hubbard-Holstein model,Heisenberg model and Electron-vibration coupling Hamiltonians, which arecritical in domains like quantum field theory, condensed matter physics, andquantum chemistry. Our implementation is available atGenesis-CVDV-Compiler(https://github.com/ruadapt/Genesis-CVDV-Compiler).