When using two amps (unlike for dual channel DI-recording into amp-sims) you need to prevent the typical ground loop that is created by dual-amp set ups in general. Please use an isolating transformer (on one channel) to interrupt the loop and prevent any AC-hum. Recommended products are the Lehle P-Iso or P-Split, the Palmer PLI-01, the Ebtech Hum Eliminator, the HUM-X or similar products. Please NEVER lift the ground of one amp at its power source to eliminate the hum. That's highly hazardous. You could become the ground and electrocute yourself.

By using an isolator you interrupt the ground loop and enjoy hum free dual amping safely.