I would not call it orbiting if the center is within the body. So, since the center of the sun-Jupiter system is just outside the surface of the sun, I would say the sun and Jupiter orbit the center of their system, but since the center of the sun-earth system is within the body of the sun, I would not say the sun orbits the center of this system. The path the sun takes in this system is entirely contained within its body.
Now, since the sun, Jupiter, and earth are all in the same system, there’s even less reason to say the sun orbits the earth, since the earth has a negligible effect on the sun’s motion.