An A321 flight crew--distracted by weather; a call from the cabin about an ailing Flight Attendant and simultaneous clearances for an off route holding pattern and a further descent to FL220--mistakenly set the altitude alert window to FL200 and an altitude deviation and traffic conflicts ensued.

Narrative

While in the descent a Flight Attendant called to advise an aft Flight Attendant was ill and being treated by a doctor. When the Captain was finished talking to the Flight Attendant; the Center called with a further descent to FL220 and holding instructions at a fix not on our route. The Captain dialed in FL200 [in the altitude alert window] by mistake and we both missed it. At about FL214 ATC gave us a traffic alert and told us we were supposed to level off at 220. Captain turned off autopilot and climbed immediately back up to 220. We got as low as 213. We also got a TA from the TCAS. We saw the traffic ahead at approximately four miles away.This event was caused by many simultaneous distractions. [We were] dealing with a medical in the cabin; a descent and a holding clearance all at once. The off route holding was a bit confusing at first. We were already close to the holding fix and had to figure it out quick. ATC was very busy and we couldn't get through to ask a question about our holding instructions. We got complacent with altitude assignment. We simply got overloaded all at once and missed the Captain's mistake on ALT knob.