Regarding the Earth and Moon, perhaps even more relevant than the mass ratio is the fact that the Moon's orbit relative to the Sun is always concave. The Moon is the only known planetary satellite for which this is always true. Perhaps that enhances the candidacy of the Earth-Moon system as a double planet. Ultimately it's a matter of semantic context. In one context the Earth and Moon could be considered adjoining planets that orbit the Sun in perpetually nearby concave heliocentric orbits while perturbing each other. In another context the Moon can be considered a satellite of the Earth, especially since their barycenter lies within the Earth.