I went with a similar solution to what NumberXaero posted and it worked fine. Thanks everybody for your effort!

If you want to have a better understand why NumberXaero method works is because you are not accumulating the rotation over time. The reason why you get this weird tilt is because i bet you were doing rotation*=currentRotation, so the tilt you were getting is correct. By rebuilding the rotation matrix you change the order in wich the rotation are applied which in terms give you the correct orientation.

Interesting... will it not brake camera rotation aroud itself? I know that just changing the multiplication order also gives this effect, but it brake camera rotation on 360 degrees and make it rotation not arount itself, but around "north and south" poles and also flipping on 180 degrees on the each pole.