The iPhone does have a normal jack for headphones (3.5mm, 1/8"). It is recessed so you need to make sure you can fit your current headphones into the jack.
If you have access to an Apple or AT&T store, I would take your headphones in and try plugging them in. Make sure you are able to actually hear music through the headphones. Sometimes headphones look like they fit, but aren't actually plugged in all the way.
If you find your headphones do not work, you can buy the Griffin or Belkin headphone extension cable for the iPhone. That or find an old 1st generation iPod Shuffle case from Apple. That includes an extension cable that will work with the iPhone also.