Mixed quantum-classical spin systems have been proposed in spin chain theory, organic chemistry, and, more recently, spintronics. However, current models of quantum-classical dynamics beyond mean-field approximations typically suffer from long-standing consistency issues, and in some cases invalidate Heisenberg's uncertainty principle. Here, we present a fully Hamiltonian theory of quantum-classical spin dynamics that appears to be the first to ensure an entire series of consistency properties, including positivity of both the classical and quantum densities, and thus Heisenberg's principle. We show how this theory may connect to recent energy-balance considerations in measurement theory and we present its Poisson bracket structure explicitly. After focusing on the simpler case of a classical Bloch vector interacting with a quantum spin observable, we illustrate the extension of the model to systems with several spins, and restore the presence of orbital degrees of freedom.