Interest in the use of magnetized targets to enhance energy multiplication in inertial confinement fusion has recently been revived after being ignored for some time. The addition of an externally applied magnetic field to a fuel volume to reduce thermal conduction losses represents one approach. The other approach is the subject examined, namely, self-generated fields created inside a target by beams that enter the pellet through a hole. The field, current, and pressure profiles in a two-region spherical plasma that might be representative of the magnetically insulated inertial confinement fusion concept are calculated in a self-consistent manner. The existence of a quasi-equilibrium soon after the formation of the plasma in the target is assumed, the appropriate magnetohydrodynamic equations in a multiregion plasma configuration are solved, and the parameters for such an equilibrium are established. An energy integral is employed to study the stability of these configurations against azimuthally symmetric perturbations, and the results are applied to some experimental as well as reactor-like systems. For certain configurations and input energies, such systems can be stable for the length of the burn.