Sounds to me like you would be better off with a touring or cyclocross bike, then. These types of bikes generally have large '700c' wheels which can be fitted with either narrow and hard racing tires, or relatively wide and robust soft touring or knobby off road tires. They generally have 'drop' style handlebars like a racer, which allow multiple hand positions and most people actually find more comfortable than flat or riser bars after you start riding for more than a few miles.
Another type of bike that might be suitable would be a 'hybrid,' which are usually bikes with more upright riding positions but the same mid-width tires that can be swapped between narrow road slicks and knobbies.
Mountain bikes can also be suitable on the road, if they are fitted with street or slick tires.
Hybrids and mountain bikes generally have handlebars that are almost stright, or have a slight rise. THese generally only have one hand position, and are generally considered not-as-good for long distance riding. Bar-ends (extensions on the ends of the handlebars) and different types of bars that allow more hand positions are common.