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