In good weather, (Visual Meteorlogical Conditions) the departure must be airborne (nose wheel off) prior to the landing a/c crossing the threshold. It may have been that your perspective on the ground made it look like this was not achieved. Aspect, distance from the aircraft, ambient light conditions etc. can affect the overall appearance of the situation.
In IMC, generally, the departure must be rolling by time the lander is 2 nm final, and by one minute's time from the point the departure began it's takeoff roll there will be a minimum of 3nm between them.