The Special Event cards all indicate they may be played "at any time". Are there any restrictions to "any time", i.e. in the middle of someone's turn? Suppose an epidemic card has been drawn -- can the airlift card be played while the epidemic steps are being applied?
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.
In a more recent BGG thread concerning the 2nd edition, the designer has clarified this rule further (be sure to check Matt's second post there).
In short, in the 2nd edition at least, you cannot use a special event card after an epidemic card has been revealed, until the epidemic process has been fully played out. An exception to this is the "Resilient Population" card, as stated on the card.