you can go one of two routes if you want something inbetween a road and mountain bike. Option 1 is a hybrid an example would be the Gary fisher 8.4ds or a similar type of bike from another brand. These bikes are more like a mountain bike than a road bike but have 700c wheels (road) wheels, and can take road or mountain bike tires. These type of bikes typically have a front suspension.
http://www.trekbikes.com/us/en/bikes...series/8_4_ds/#

Option 2 would be a cyclocross bike. A cyclocross bike is more like the road bikes because it has a road frame but is built to take more abuse and is typically heavier than a similar road bike. An example would be the Specialized crux or tricross.
http://www.specialized.com/us/en/bikes/road/crux
http://www.specialized.com/us/en/bik...tiuse/tricross

There are some other options that I'm sure people will kick around for you. Touring bikes or some others but I don't know much about them so Ill leave that to some other members. If you haven't been to a local bike store be sure to stop in and ask questions and test ride a few different styles of bikes, ultimately that will determine what kind of bike would be best for you.