The magnetohydrodynamic (MHD) stability of a streaming annular jet having a solid rod as a mantle, subjected to the capillarity, inertia and electromagnetic forces is presented. An eigenvalue relation valid to all axisymmetric and non-axisymmetric disturbances is derived. The (in-)stability characteristics of that model are identified analytically and confirmed numerically for numerous forms of the (interior and exterior) magnetic field, the radii ratio of the solid rod to the fluid cylinder and the basic flow velocity. There were unstable states to non-axisymmetric disturbances due to the strong destabilizing influences of the streaming and the vacuum varying magnetic field. The required restrictions for the stability are determined and several special cases are studied. The thicker the solid cylinder so the greater its stabilizing influence and the MHD non-streaming annular jet is absolutely stable. However, the streaming destabilizing effect will upset that situation and there will be unstable states not only to axisymmetric but also to non-axisymmetric disturbances. Due to the strong stabilizing influences of the interior field and the curvature pressure on the very thin annular jet, around a very thic' solid rod, the (in-)stabilities are slowed and more easier observations are expected to be allowed than in the case of the full jet and also than in the case of the annular jet having a gas-core jet.