Is it possible to create an iron door which responds to levers on both sides

Solution 1:

I would suggest using buttons instead of switches. You push a button, the door opens, then the button deactivates, closing the door.
It's true that the delay is really short, maybe not even enough for you to get through. This problem can be solved using repeaters to build circuit delaying the closing signal. I currently don't have enough time to try and build a working solution, but if you won't figure it out on your own by then, I'll do my best to update this post later in the day.

Edit: Just for for the sake completeness: instead of buttons, you could also use pressure plates. Just place one in front of the door from both sides. Be wary though, because mobs can also trigger them. (I almost lost my mind once, when I had a door wired like this and a damn chicken kept stepping on the plate and banging with the door. I had to replace the plate with a button.)

Solution 2:

You can use a XOR or XNOR gate which will make the output change to either switch.

They look like this in Minecraft:

XOR gate:

XNOR gate:

Solution 3:

Rory, I use an adjacent open block with a lever on the top to solve this:

    @@@
    @xL
    @x@

Where 'x' is door, '@' is a solid block, and 'L' is a lever. So the top of this block can be reached from both sides.