A tire can be balanced but still not be smooth riding. Technically, you could balance a square tire if you really wanted to and one existed, but it wouldn't ride smoothly. Even if a tire is balanced it can still have high and low spots that will make it bounce slightly at certain speeds. This becomes even more noticeable on larger tires. If you have any worn suspension components they can move around slightly and make a small movement from the tire feel larger than it is.

It sounds like you may have got some out of round tires - a good shop should be able to do a road-force balance on them and remount the tires on the wheels so the highest weight positions on the tires are aligned with the lowest weight positions on your wheels to minimize the vibration. You will probably need to look for any slop in your front suspension and steering and replace any worn parts before you'll get it to ride smooth again.