The Sun won't pass between the Earth and the Moon in the near future, because the Sun is so much further away from the Earth, than the Moon. When the three are nearly co-linear, either the Earth blocks sunlight to the Moon (a lunar eclipse), or the Moon blocks sunlight to the Earth (a solar eclipse). But just because this is impossible in the near future, doesn't mean it is impossible forever!
Gastineau and Laskar have long term orbital models in which the orbit of Venus expands to reach the Earth. Their paper in Nature is unfortunately behind a paywall, but there is a nice article here, that includes a diagram for a potential orbital scenario of the Solar System in the future.
Here, the green orbit is Earth's path and the blue orbit is Venus's path. I used this as a taking off point for my answer and ran a simulation in which Venus passes close to the Moon and causes the Moon to achieve escape velocity from the Earth. In it's new orbital path, the Moon has a slower orbital period than the Earth, and in less than 10 years is on the opposite side of the Sun from the Earth. As mentioned in the other answer, this would most likely be known as a Solar Occultation, but in the remote possibility that a sentient species was still alive, I imagine they would have a special term for this extraordinary event!