Upon revisiting the Hamiltonian structure of classical wavefunctions in Koopman-von Neumann theory, this talk addresses the long-standing problem of formulating a dynamical theory of classical-quantum coupling. The proposed model not only describes the influence of a classical system onto a quantum one, but also the reverse effect – the quantum backreaction. These interactions are described by a new Hamiltonian wave equation overcoming shortcomings of currently employed models. It is shown that the density matrix of the quantum subsystem is always positive, while no such general conclusion is yet available for the Liouville density of the classical subsystem. The proposed hybrid description is illustrated on the exactly solvable example of a degenerate two-level quantum system coupled to a classical harmonic oscillator.