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human
Is it possible to have a planet and a moon in close enough proximity that their atmospheres mix?

I'm thinking of planets something like Pluto and Charon (yes, I know, Pluto's not a planet) where you have 2 large objects spinning around each other in fairly close proximity.  Assuming that these 2 objects both have an atmosphere, would it be possible for these atmospheres to mingle?  Or would an orbit that close together be unstable (due to atmospheric drag perhaps?).

I'm writing a science fiction story where it may be possible to travel from the planet to the moon while remaining in atmosphere (albeit, a very thin atmosphere).

EDIT:

What about if I introduce a third body?  A planet, a moon with a very elliptic orbit and a second much further out moon.  The closer moon's elliptic orbit would usually carry it close to the planet at perigee, but not close enough for their atmospheres to touch/mingle.  But once every thousand orbits or so the second moon would influence the other's orbit enough to make it dip closer to the planet (lets say a couple of thousand KM of the planets surface, for argument's sake this is a large planet with a deep atmosphere), then on the next orbit it would "straighten it back out again".

Could this be stable?  Would tidal forces rip the moon apart?  Would the constant drag in those once-in-a-thousand close passes be enough to destabilize the moon's orbit and send it crashing into the planet (or slingshot it out to space)?

For the sake of the story this has to be a stable arrangement that has existed for untold millions of years.  Also the close passes would have to be within living memory (a couple of thousand years apart would work, maybe as far apart as 10,000 years).

As a side note, I suppose I'll have to write in that at perigee whether or not the atmospheres mingle the moon's gravitational influence would cause massive tides, increases in volcanism, and just general doomsday scenarios.  Actually, this would work out very well in the story.
gpt
This is not possible in the long term, at least not for planets. Let's consider that the atmosphere always remains aerodynamically flyable by a suitable craft, which is around 100 km on Earth (depends on the design of the craft really, but air density has a big say in it). It's less on Mars and more on Titan.

So let's put Titan in orbit around Earth and have their atmospheres touch. Interesting things happen here, as we've really caused both objects to overflow their Roche lobes. Do the math, and you find that the surface of Titan is 500-900 km from the surface of Earth. That's very low!

Things get really exciting really quickly. Earth, being more massive, strips atmosphere from Titan. It's a slow process, but eventually Titan would have no appreciable atmosphere left. It won't get this far, though. It'd need around half a million to a million years, and we don't have  that time.

The most exciting thing is the tidal effect. Being in a prograde orbit at 3,400 km (Titan's radius is 2,500 km), it orbits once every 115 minutes, rising in the west and setting in the east, really whipping around Earth. It raises, depending on location, 1 km to 5 km water tides and a 100-200 metre land tide. This causes cataclysmic earthquakes and complete volcanic resurfacing of both bodies, but more fun is still to come.

As Earth rotates much more slowly than Titan is orbiting, it sweeps the tides back a little, causing slight concentrations of mass just behind where Titan is in its orbit. This pulls Titan back ever so slightly, speeds up Earth's day a little, and lowers Titan's orbit. After around 50,000 years, Titan has experienced so much tidal drag that it gives Earth a nice big hug. The disintegrating Titan will smear itself around Earth's equator, leaving a trail of 10 to 100 km deep, 800 km wide gouges down to the upper mantle, boiling the atmosphere and leaving behind fractured, smashed terrain. It's not so much an impact crater as a complete obliteration of Earth's entire surface.

So in short, yes you can do this, but you don't want to be anywhere near either of them if you do.