People in the US normally treat each lane as a discrete entity, and passing on the right/inside lane is as acceptable as in the left/outside lane or the center/centre lane. Exceptions do exist, such as in Texas where the freeways are posted "Left lane for passing only". Slower drivers do not keep to the right/inside (the rat bastards).

Beware of signs that say "right lane exit only". This means that the right lane goes on to the off-ramp, and there is no option to stay on the main road without a last-moment lane change. This tends to be difficult if there is a large truck to your immediate left.