The fact that you are seeing the high beam indicator light coming on shows that you are getting current to both that bulb and to the high beams. They headlights use a different ground so maybe that is where you can find the loss of your circuit.
You could try unplugging one bulb and see if the other bulb works. I think the relay is located on the fuse panel but if you have an owners manual it might give you more detail. The other possibility could be that the switch has gone bad and has an open in it due to corrosion or arcing that has built up internally.
here is a link to a wiring schematic:
http://repairguide.autozone.com/znetrgs/repair_guide_content/en_us/images/0900c152/80/07/d4/c3/large/0900c1528007d4c3.gif