You can set up most good bikes to work in most situations. My older road bikes take size 28 and 32 tires, and provide good riding on dirt "mountain bike" trails that are in reasonably good condition. And, my mountain bike works great on pavement with light "slick" tires.
The bike messengers in downtown Houston use every kind of bike there is. But, among the more experienced messengers, a popular bike is a mountain bike with slick tires. They can take the beating that pot-holes and curbs dish out. The wheels are strong and remain true. The fatter tires provide a good cushion to protect the rider from road shock.
The road bike, circa 2005 is NOT anything like the road bikes of 1985. In the old days, most road bikes were designed to handle any sort road, included dirt, or gravel, and to be tough enough to support both a rider and fifty pounds of gear.
In 2005, the "Be Like Lance" marketing game has turned most "modern" road bikes into "pretend" racing bikes. A "pretend" racing bike will come with size 23 tires, and have short chainstays and a short wheelbase "Just like Lance rides". The stems are three or four inches lower than the saddle, forcing your weight forward onto your hands.
All of these "racing" features makes them the WORST sort of bike for the urban rider who DOES not race. The skinny tires and short wheelbase don't absorb shock well. Urban potholes break spokes and put the wheels out of true. No room for large saddlebags to carry school books, computers, a large sack of groceries, or a case of beer...some of the basic requirements of civilized life.
So, stick with your mountain bike. Put on slick tires. Put on bar ends to get another hand position. Enjoy the bike you already have.
When you get ready for another bike, look for a 1985ish touring bike. A, wide, strong 40 spoke rim in back. Designed for fat tires. Room for saddlebags both front and back for long summer tours (or trips to Krogers). The long chainstays and long wheelbase shock up road shock. A road bike designed for real roads and real riders. Usually available for under $200 or so.