Had the same set of symptoms recently on my '97 Toyota Tacoma, didn't think it was burned out bulbs because what are the odds of both of them burning out at the same time? But sure enough both bulbs were toast. For some reason one bulb burning out encourages the other one to do the same.
The reason the low beams stay on is because they are designed to do so. The low beams are 55 watts, and the high beam filament simply adds another 10 watts and changes the focal direction.
You can buy 65 watt low/85 watt high H4 bulbs. NAPA sells these, same price as standard 55/65 watt bulbs. I highly recommend them if you do a lot of nighttime rural driving - but as a courtesy to other drivers you should make sure your headlight alignment is good, and always be quick to dim 'em for oncoming traffic. They do have a slightly shorter lifetime though.
