Spawning a process: Can I "have my cake and eat it too"?

[Nick Sabalausky (Abscissa)]

I'd like to include this functionality in Scriptlike, but I don't know 
if it's even possible:

Launch a process (spawnProcess, pipeShell, etc) so the child's 
stdout/stderr go to the parent's stdout/stderr *without* the possibility 
of them getting inadvertently reordered/reinterleaved when viewed on the 
terminal, *and* still allow the parent to read the child's stdout and 
stderr?

How could this be accomplished? Is it even possible?