Here are some I read on other forums.
Protect the VIP CFN member. Land on the roof of the 25-story building and take out the aliens before they get to the Council member in his secret panic room on one of the top 5 floors. This mission pops up when a funding nation is paying you a certain high amount of funding. The aliens in this mission are few, but are the elite and will require skill to win without taking casualties. Not sure if they should be Thinmen synthoids for coolness.
Exterminate the Cryssalids Hive. An Alien base mission, but the catch is... Cryssalids only and the base will look like the hive from the Aliens movie. Impossible difficulty and prepare to use your high reaction fire operatives. To win, you have to eliminate the Hive Queen and then hold out until all the Cryssalids are dead. After you take out the hive Queen, all the Cryssalids in the Hive will come to you.
Protect the oil drilling platform. Land on an oil drilling platform in the middle of the ocean and defend it against the aliens. The funding nations depend on oil, so they'll want you going out if the UN Military fails.
That's all I remember
You wanted non-alien missions right?