We develop, test and apply a volume of fluid (VOF) type code for the direct numerical simulation of two-fluid configurations of magnetic fluids with dynamic interfaces. Equilibrium magnetization and linear magnetic material are assumed and uniform imposed magnetic fields are considered, although extensions to nonlinear materials and to fields with spatio-temporal variability are possible. Models are computed for configurations of bubbles of non-magnetic fluid rising in ferrofluid and droplets of ferrofluid falling through non-magnetic fluid. Bubbles and droplets exhibit similar changes of shape in the presence of vertical fields, due to a combination of elongation along the field lines and the fluid dynamics of ordinary rising or falling at small Bond number. Bubbles become more prolate than droplets under the same parameters and are accordingly found to break up more readily than droplets in stronger fields. Indirect effects are observed, such as the change in rise time and the consequent changes in the flow due to increased Reynolds number.