Do double planets exist?

The Earth-Moon system can be considered a double planet. The Moon’s relative mass is great. The moon is attracted by the sun more than the earth. The heliocentric orbit of the Moon is an ellipse perturbed by the Earth.
Pluto-Charon system can be considered even closer binary planet. The distance between the centers of Pluto and Charon is 20 times less than the distance between the Earth and the Moon. Pluto’s diameter is only 2 times that of Charon.