I think a cyclocross bike would fit your situation well. They're great for commuting and with slick tires they can be a decent duathalon-type bike. They're also pretty much made for taking turns too fast and eating gravel. (I do that on a weekly basis on mine during the fall.)
Within your budget, your only options for CX bikes are used and Bikes Direct (and even Bikes Direct would stretch your budget a little). Any new bike you get for under $500 is either going to be very poorly made (X-Mart) or have flat bars. Flat bars aren't really very well suited for something like a duathalon, even if you don't want to win. I also wouldn't want to do a 15 mile commute on a bike with flat bars.