The Mothership is the psychedelic Camper owned by The Truth. During the mission Black Project, the Mothership is completely indestructible (except the never-fail methods of sinking it in the water, flipping it over, etc.), and if you can manage to get it to a garage, it will retain these qualities. Here's how to do it.
Go through the mission until you get the jetpack. Instead of going to meet The Truth, fly over to Hunter Quarry and get in the crane. When you get out, the Jetpack is gone and you once again have control over your arsenal. However, you still cannot enter vehicles. If you try to get on the dirt bike in the quarry, the game will not even register that you are trying to enter a vehicle. We'll deal with this in a moment.
You will have noticed by now that there is no traffic, very few pedestrians, and very few spawned cars. There should be a dirt bike somewhere in town, grab it. As long as you're still there, hit up Ammu-Nation and get a sawn-off shotgun and some grenades if you don't already have some. Maybe grab a bite to eat at Cluckin' Bell, as the next part may take a while.
Now you should have a dirt bike, a full stomach, at least five hand grenades, and a pocket full of shells. Let's ride. Between Fort Carson and the meeting point with The Truth lies the Restricted Area. Go on back there on the dirt bike and trade up to the Patriot. (You will notice at this point that even though you are re-entering the Restricted Area, you don't get the usual five stars. This is because your wanted level is locked. Once this is all said and done and the Mothership is safely tucked away at your hangar garage, feel free to do with this information what you will. Go back to the Restricted Area and steal a Rhino, or take the opportunity to get the oysters under the Easter Basin Naval Base. The sky's the limit.)
Now that you're driving a decent car, get to The Truth. He's waiting at the top of Arco del Oeste. If you don't want to mess your Patriot up just yet, go ahead and leave it at the road. It's not going anywhere. Get up the hill, but do not go into the red ring. Push the Mothership over the ledge toward the east (in the direction of the road, and more importantly, the Verdant Meadows garage), or shoot it off with the sawn-off if you're getting impatient. Note that the Mothership may become lodged in between the rock formations at the bottom of Arco del Oeste; that's why we brought the sawn-off shotgun. Shoot it or push it until you get it to the road. Note that the Mothership may land face-down and explode. Don't worry about it. Once you get it into your garage, it'll be good as new.
Now all that's left is to push it to Verdant Meadows with your Patriot and get it into the garage. Once this is done, kill yourself with the grenades to fail the mission. (Tip: if The Truth is still in the Mothership, which he may be, make good and sure you've wedged the Mothership into the corner, or he will try to drive away when you die.)
You'll spawn in Las Venturas; drive on back to the hangar, verify that the Mothership's in the garage, go ahead and shoot the gas tank if you want to make sure it's really invincible, and save your game. Done and done.