The structure and dynamics of diffuse gas in the Milky Way and other disk galaxies may be strongly influenced by thermal and magnetorotational instabilities (TI and MRI) on scales ∼ 1 − 100 pc. We initiate a study of these processes, using two-dimensional numerical hydrodynamic and magnetohydrodynamic (MHD) simulations with conditions appropriate for the atomic interstellar medium (ISM). Our simulations incorporate thermal conduction, and adopt local “shearing-periodic” equations of motion and boundary conditions to study dynamics of a (100 pc) radial-vertical section of the disk. We demonstrate, consistent with previous work, that nonlinear development of “pure TI” produces a network of filaments that condense into cold clouds at their intersections, yielding a distinct two-phase warm/cold medium within ∼ 20 Myr. TI-driven turbulent motions of the clouds and warm intercloud medium are present, but saturate at quite subsonic amplitudes for uniform initial P/k = 2000 K cm. MRI has previously been studied in near-uniform media; our simulations include both TI+MRI models, which begin from uniform-density conditions, and cloud+MRI models, which begin with a two-phase cloudy medium. Both the TI+MRI and cloud+MRI models show that MRI develops within a few galactic orbital times, just as for a uniform medium. The mean separation between clouds can affect which MRI mode dominates the evolution. Provided intercloud separations do not exceed half the MRI wavelength, we find the MRI growth rates are similar to those for the corresponding uniform medium. This opens the possibility, if low cloud volume filling factors increase MRI dissipation times compared to those in a uniform medium, that MRI-driven motions in the ISM could reach amplitudes comparable to observed HI turbulent linewidths.