Not all, it depends on the 'offering' airline itself. Some have agreements with individual carriers on thier own, some are included through US if the carrier extends the privelege to Express affiliates. A quick look through our interline and ZED agreements shows that some include mainline and wholly-owned only, some include parents some don't, some include companions and some don't. Agreements between carriers vary quite alot.
None of the Express carriers US Airways works with have cabin seat agreements with Southwest. JetBlue has always had a very easygoing policy, they seem to let anyone but Osama Bin Laden board as a jumpseat rider.
OAL non-revs are relatively rare, as it's often a time consuming and confusing process. Official cabin jumpseating between carriers is pretty new, at least on this scale. US Airways (the airline, not the collection of carriers that wear the name) is actually kind of at the forefront of this, which is terrific. Let's hope a few idiots don't ruin it for all of us, and lose us our current agreements or prevent future ones. We are already the laughingstock of the industry without some of our stupider employees getting us thrown off other carriers.