After bonding, is there usually a visible line between the actual tooth and the bonding? Is this normal? Can it be fixed?

Yes it can be fixed. Your dentist needs to create a long bevel on the tooth surface adjacent to where the fracture is. This does not require a lot of tooth structure to be removed and allows the composite to blend into the body of the tooth. He can also place tint along the line of the fracture before the composite is placed.

Sounds like your dentist was trying to be conservative and save as much of your tooth as possible. If you want improved esthetics, then I agree with what your dentist is telling you....he would have to drill more of the surface of the tooth away to better match the color and cover over any underlying defects. Direct composite fillings can be very challenging to match perfectly. It's not something that is taught in great detail in dental schools, and great cosmetic dentists undergo extensive training to take composite bonding to a higher level.You do have another alternative, however, which would probably give you a better result, be stronger, and much more likely to give you a longer lasting result. Did your dentist give you an alternative treatment by doing a porcelain veneer? Porcelain veneers are much stronger than direct composite bonding, but will cover the entire front surface of your tooth.

Bonding to front teeth is technically difficult but with some perseverance that line won't be visible. It involves creating a beveled margin so there isn't a definite line where the bonding ends.