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We explore the effect of magnetic fields on the vertical distribution andmultiphase structure of the supernova-driven interstellar medium (ISM) insimulations that admit dynamo action. As the magnetic field is amplified tobecome dynamically significant, gas becomes cooler and its distribution in thedisc becomes more homogeneous. We attribute this to magnetic quenching ofvertical velocity, which leads to a decrease in the cooling length of hot gas.A non-monotonic vertical distribution of the large-scale magnetic fieldstrength, with the maximum at |z| $\approx$ 300 pc causes a downward pressuregradient below the maximum which acts against outflow driven by SN explosions,while it provides pressure support above the maximum.

The supernova-regulated ISM -- VI. Magnetic effects on the structure of the interstellar medium