Al B wrote
The real question I'm trying to get an answer to has to do with
whether there is any required horizontal separation of passenger
jets that are flying at different flight decks.

If adequate vertical separation exists, no lateral separation is
required.
Vertical separation between airliners flying under instrument flight
rules (IFR) is normally 1,000'. The vertical separation of IFR
jetliners and general aviation aircraft flying under visual flight
rules (VFR) is normally 500'.
There is NO separation required for two VFR aircraft except to not
cause a collision hazard.

Bob Moore
ATP CFI