I see there has been no update to any of the walkthroughs for this mission, and I just figured out how to properly (with stealth) complete it, so I'll go ahead and add the info that is missing from the walkthroughs.
This mission not only requires that YOU never be seen, it requires that no unconscious or dead guard you take out is seen by any other guard. You CANNOT have any body seen, or it triggers a general alarm. You will know if you have triggered it, because the civilians will start panicking and jumping out of windows to get away from you, and the guards on the top floor (the room opposite the study) will begin to search for you (you should be able to hear them moving around upstairs if you have units in the house).
make frequent saves, and if on your turn, civilians panick, or you see those upstairs guards move.... reload because it means someone saw one of your bodies.
Don't even bother with trying for the stealth complete unless you have a unit with at least 70 stealth, preferably much higher even!
for best body removal... have your best stealth unit move as close as possible to your target BEFORE you use knockout darts or stealth weapons. then make sure your stealth unit moves the body out of the potential sight lines of ANY guards (that means being patient, and monitoring how the guards do their patrols, especially in front of the house, where there are 3 patrolling guards, and two mercs standing outside the door (with body armor). that brings up another point. The two mercs standing outside the front door MUST NOT EVER BE ATTACKED, or it will trigger a general alarm (you can, however, take out the two mercs standing outside of the complex main gate, provided you can take down both of them on a single turn without being spotted; it's not that hard. one of them drops a nice rocket launcher and ammo). Yeah, that's right, you're gonna have to sneak past them... not only that, but you have to sneak past IN FRONT of them. Why? well, because if you try to enter the main foyer on the first level (where the stairs are) via the door near the bathroom, you will get spotted by a russian soldier standing underneat the nearest stairs. you might get lucky and sneak past him, but even with 97 stealth, I could not. I think you are not supposed to.
ok, what that means, is that you have to take out all the patrolling guards in the front courtyard area. other than the two standing by the car, 3 are actually on short back and forth patrol routes, so you will have to take them out one at a time, and quickly move the body before the next patrol can see it. Again, a scout with good stealth should be very close to the target when you take them down, then run them out of the patrol route towards the outside main gate (dropping them just outside the gate works. if the gate is open, the door will block the view of the mercs there if you didn't take them out). I found that Shade (if you found and leveled him up a bit) is perfect for this task, as he can both stealthily take down a guard with shurikens or throwing knives (or a dart pistol) and be right next to them when they drop so you can also start hauling the body away.
Taking the three patrolling guards in the front courtyard out without any bodies being seen is by far and away the hardest part of this mission. If you manage it, the rest is gravy.
ok, assuming you have taken down all the guards in the courtyard, take your stealthiest unit, and belly sneak as close to the edge of the wall in the courtyard as you can, and you should be able to sneak past the mercs standing by the front door. Once past them safely, enter the window of the room on the right of the front door (facing the house). you can safely move to crouch position now. move to the door of that room that leads to the foyer, but make sure you have full AP before you open it (wait a turn if not). open the door, and you should see a russian soldier standing under the stairs on the far side of the foyer from you. this is the last guy you need to take down stealthily. use whatever means you choose (killing is fine, so long as you are quiet).
Whee! that complete the hard part of the mission. now you can bring in whatever stealthed guys you have through the other door in the foyer. but really, all you need from this point is your PC, an engineer, and maybe one more guy to haul loot.
move up the stairs and pick the lock on the door to the left, and then the chest in that room; grab all the fine cash goodies. Now, take your engineer and have them climb up the ladder near the entrance to that room. unlock the door at the top. turn left and you will see a trapped chest. disarm for a very nice grenade, then pick the lock for DP machine gun (if you don't already have one). leave that room and go across the floor to the room opposite and pick that door lock. there's another trapped chest with goodies, and a medical locker to pick. you can collect this loot now, or wait until you reach the leave area; it will all be available. go out of that room, and up the second ladder just outside it to the narrow storage area, at the end of that is a nice suit if you want it.
ok, all locks picked, traps disarmed, etc... done NOW, because you will NOT be wanting to come back this way soon.... move all your units except your PC back downstairs, and OUT of the foyer area (side rooms are ok, so long as the doors are closed). take your PC and sneak them to the door to the study (it's the door on the left-front of the second floor, above the room you entered the house in after sneaking past the front door mercs) .
if you are in sneak mode with your PC (MUST be PC; no other unit will work) when you reach that door, a cutscene will trigger.
gratz! you have completed the stealth objective.
now, after the cutscene, DO NOT TRY TO SNEAK BACK DOWN THE STAIRS. there is a new guard right by the ladder that leads to the attic that will detect you unless you have near 100 stealth. There is one last chest in the room diagonal from the study on the same floor, just walk over to it and picklock the chest there. Whee! lots of cash, and a nice suit on the bed you might want too. Now, move back out to the room just outside the study, and go to a window on either side of the window directly over the front door. open it, move right to the edge of the windowsill facing out, and click on the ground one level below you. you will jump out the window to the ground and take a couple of points of damage. House exited!
lastly, move your PC to the exit arrow, which is exactly where you started the level. then, one at a time, move the rest of your units to the arrow. As the last one reaches it, your objectives will all be complete, and you can leave. ALL the goodies from chests, guards, etc; everything you saw during the level, will be there for you on the leave screen. if you left some room to carry crap, your haul here will be nearly 100K! for some weird reason, the exit area doesn't always trigger correctly, so make sure to move your guys there one at a time. if it doesn't work, exit the game entirely, reload, and move your units one at a time there again.
your mission reward money will be exactly double (the main mission money, and that again as bonus for a nice total of over 8k!)
congratulations on completing the most irritating, tedious, slow thief-clone mission ever.