As, I have been using a Double Fisherman's knot to join the two ropes. With some physics that I know, in Double Fisherman's knot the same amount of pressure (stress) is applied over the two turns of each rope, so making sure there is no significant damage done to any of the rope.
However I believe that if the two ropes are not of equal thickness, or may be say if the difference between the thicknesses is a considerably huge, Double Fisherman's would(?) do some damage to the thinner rope.
In that case how trustworthy are Sheet Bend and Zappelin Bend?
Edit: I am Not going to use this for rappelling at all. I intend to use that as a holding line when me and friends are swimming in a lake nearby. Having said this, We are not entirely relying on this as well.