Unitary integration is a numerical method that preserves the structure of the quantum Liouville equation by evolving the density matrix r via Unitary integration is a numerical method that preserves the structure of the quantum Liouville equation by evolving the density matrix r via unitary transformations. Unitary integrators preserve the kinematic invariants c_j = Trr^j, j = 1,..., n to all orders in the time step. Here we extend our previous work to interacting systems and to dissipative systems. We take as our prototypical interacting system a two-level atom interacting with a single mode of the quantized electromagnetic field. We approach dissipative quantum systems by adding a dissipative term -Lr to the density matrix equation and applying the technique of operator splitting. We use a unitary integrator for the Hamiltonian evolution and a conventional integrator for the dissipative piece. In this way we guarantee that all dissipation and decoherence (variation of the c_j) is due to the new non-Hamiltonian terms, and not to any numerical artifacts.