Special event cards and timing
This question was answered by Matt Leacock, the designer of Pandemic, on BoardGameGeek:


  You can play the cards at any time, however, you can't play them
  between an event and the representation of the event on the board.
  Some scenarios may help explain this:
  
  Scenario 1: Player #1 has a Special Event card for "Resilient
  Population." During the draw, an Epidemic card is drawn. Since an
  Epidemic card was drawn, player #1 decides to play their Special Event
  card to remove a city from the infection discard pile before they are
  reshuffled. This is legal because the card was played before the cards
  were reshuffled.
  
  Scenario 2: A player may use the Forecast card to rearrange the cards
  on the top of the infection deck before they're drawn -- but once a
  card is drawn, the player can't rearrange the cards.
  
  Scenario 3: The Red disease has been [cured but not eradicated]. A player draws the
  Taipei card which results in the 8th outbreak. Since no time elapses
  between the drawing of the Taipei card (resulting in the infection)
  and the placing of the cubes (representing the infection), the players
  lose the game. It's not OK to Airlift the medic over to Taipei to cure
  because the cubes have already been added and the game has already
  been lost.


So in your specific example, yes you can play the Airlift card, if you do so between Epidemic steps.