Air carrier First Officer reported that during descent they experienced icing conditions; and the number 2 engine indicated high vibration. While trying to resolve the problems; they overshot the crossing altitude.

Narrative

Whilst beginning the descent via the STAR; we experienced icing conditions and Engine 2 started to experience high vibrations (4.1). I noticed this immediately as pilot monitoring and informed the Captain; who was pilot flying. He passed control over to me and proceeded to go into the QRH. We worked together to resolve the issue; passing the controls back and forth a total of two times. During this event neither of us had realized that the aircraft was in the wrong automation mode and would not respect the crossing altitudes. As soon as the aircraft had gone through the altitude we noticed and corrected.Cause: Task saturation. Captain used VS mode to expedite the descent in order to get us out of the conditions that were causing the event; however; I failed to notice that we were in an automation mode that did not respect crossing altitudes due to task saturation. Suggestions: Smoother passing of controls. Ensuring the aircraft is in the desired automation before passing over or being clearer as to what mode is currently being used. Instead of passing controls back and forth; as pilot monitoring initially; I could have been the one to read the QRH; reducing the number of role swaps and; therefore; chance of miscommunication.