coplanar transmission line on both sides of a four layer board
First I would ask why a coplanar waveguide?  Given that you have a four layer board I would think using micro strips would be easier / better.

Based on your Stackup you are really talking about a conductor backed coplanar waveguide.  In that case return current will flow on both your side conductors and the "reference" plane underneath them.  I say "reference" to emphasize that on the bottom return current will flow in your vcc plane and your side conductors.  In a micro strip it would flow just on vcc.  This is because this path is the path of lowest impedance for the current to follow.

Now current flows in a loop so when it gets back to the source it must find a way back to gnd to complete the circuit so it will find a way.  In a well decoupled board that path will be the nearest decoupling cap(s).

A good source to learn more is the handbook of black magic by Dr Howard Johnson, his website, Eric Bogatin's books or website, and Brian Waddel's transmission line book.