Numerical simulations of the multi-phase interstellar medium have been carried out, using a 3D, nonlinear, magnetohydrodynamic, shearing-box model, with random motions driven by supernova explosions. These calculations incorporate the effects of magnetic fields and rotation in 3D; these play important dynamical roles in the galaxy, but are neglected in many other simulations. The supernovae driving the motions are not arbitrarily imposed, but occur where gas accumulates into cold, dense clouds; their implementation is determined by a physically motivated model for the evolution of such clouds. This model is thus self-regulating, and the overall supernova rate is not an input parameter, but arises as part of the solution. Simulations with differing mean density show a power law relation between supernova rate and density, consistent with observations. The global structure of the supernovae-driven medium is strongly affected by the presence of magnetic fields.