You are wrong that aircrafts and rockets are lighter than air. It’s just that it uses the power from the engine to go through the air, otherwise both aircraft and rockets are heavier than air.
Airplane uses engine powers and rocket uses rocket engine boosters to operate and penetrate the air, which might give you the illusion that aircrafts and rockets are lighter than the air.
In fact, An aeroplane (airplane in US usage), is defined in ICAO Document 9110 as, "a power-driven heavier than air aircraft, deriving its lift chiefly from aerodynamic reactions on surface which remain fixed under given conditions of flight".