Their goals are the same, to destroy the world. If the Thalmor could somehow find a way to control the Falmer, heck even if they couldn't. If I was the Thalmor I'd be rounding up all the Falmer I could find and just let them loose on the world.

This idea is far more evil than Alduin and his fate alone.

Where do you get he Falmer want to destroy the world?

A loading screen mentions how they hate and want to destroy all that live on the surface.
Though I think the Falmer would just wind up killing the Thalmor who went down there...Home turf advantage, language barrier, and I doubt the Falmer give a [censored] about the Thalmors plans.

There would be no allaince.

Falmer are (currently) xenophobic trogdolytes who hate all life above ground and wish it destroyed.

Thalmor are elitists, and would likely see the Falmer as little more than beasts. They only wish to complete remove the Idea of Man from Tamriel, and if it so happens that it causes Tamriel to explode, so be it. Or they wish to return everything to a pre-creation state (thus destroying Tamriel,) which they view as a "better" life than mortal existance. Or they wish to ascend to godhood, and destroying Tamriel is a side-effect of that plan. Hell, it could be all three.

It's not about political allegiances, it's about what the potential damage the Falmer could do. I doubt the Falmer care about the Thalmor about as much as they care about dragons. All I'm suggesting why don't the Thalmor let the Falmer do some of the work. They're a crazy blind underground army, just let them loose on the world above and all the Thamlor have to do is stand back and watch.

Since the Falmer are blind anyway, no way they can read the road signs and figure out where they're going.

Sounds like a win-win situation.

I give the Thalmor a little more credit to stop sending Emissary Squads down into the dark corners of the earth after the first three vanish.

How are the Thalmors supposed to pick them up deep inside their lairs? Ain't nobody got time fo dat.

Nah, the Falmer would kill the Thalmor, if the Falmer decided to wage war on the surface then the Thalmor would also be targets. Then again all we need are highly skilled assassins who have silent enchantments and sneak attack each Falmer since the Falmer are blind, perhaps even get some scent masking stuff.

Truthfully all we would need are giants, Thalmor and Falmer alike would be flying in the air.

The Falmer's first target would be would be the other mer.
They are too,twisted to actually make alliances,They would hate any of the "Surface Dwellers"