I just had the same sort of thing happen to my 2001. 5 2500 sport model(it has the 2 bulb headlights). I was driving back late at night from Houston after helping folks with hurricane Ike cleanup. Since I drove down the night of the hurricane, right after it passed, I had been driving with High Beams on for many hours. About an hour from Austin, lost headlights. Fogs still worked so I went slow, drank lots of coffee, and got back no problem. I checked relays, and all were good. Checked batteries, same, no problems. Strange symptom was that while I had no low beams, I could bull the stalk back like I was engaging the high beams, which would go on as long as I held the stalk back, but would not stay on permanently. Went to Advance auto and bought a new turn signal switch as this was suggested after I confirmed that the actual headlight switch was fine, and in testing that, found that the green with white stripe wire had totally overheated at the factory plug that leads to the switch assembly, and broken off at the pin connector. It clearly had happened a few times as the white connector body was melted some too and the wire insulation was brown for an inch and a half or so back from the connector. I tested to see if I had a short, found nothing(no blown fuses either), and used some tools I have to remove the pin from the harness connector, cleaned it up, soldered a new section of wire to it and spliced into the harness back where the wire was good with no charring or corrosion from the heat, and have had no problems since.
This might be a place for you to look too.