I suppose you could call the part between the crosshead and the crown a second conrod, but I prefer to think of a crosshead design as an articulated piston with a particularly large clearance between the crown and skirt, the corresponding large compression height, and a crown that has a different diameter than the skirt.
You might be able to find some useful information on the subject if you compare articulated pistons to mono-block pistons, and keep in mind that a crosshead design is like an extremely exaggerated version of the articulated design.
In some designs, the crosshead piston will have a crown that's rigidly attached to the skirt (no relative rotation), in which case the articulated analogy no longer holds (an articulated piston allows relative rotation between the skirt and crown).
The advantages / disadvantages will depend on the particular application, but here are some that come to mind:
good
* The crosshead (piston skirt) can run in a different-size bore than the compression portion (piston crown), which allows a larger bearing area on the skirt.
* works for very high cylinder pressures (due to above)
* The crosshead will be thermally isolated from the crown
* The crown experiences very little thrust loading, and can get by with little or no lubrication (useful for extremely high temps or "clean" applications)
bad
* bulky design, eats a lot of space between the crank axis and the top of the piston
* heavy
* The conrod angularity is increased (for a given package height), so the crosshead (skirt) needs more area to carry a given cylinder pressure.