Are mixed classes possible on a single ticket for a single passenger?
score:7
Accepted answer
Yes, it's entirely possible, and since Delta and Korean are both in Skyteam the itinerary is quite feasible. However...
Tickets like these are usually impossible to book online, you will need to book this directly with the airline or a travel agent. (Update: There are exceptions, and Delta appears to be one of them!)
While price difference between economy and business for ICN-CEB alone may well be $1000, if you're travelling all of BNA-DTW-ICN in business class, the cost difference for upgrading the final ICN-DEB leg as well is likely to be lot less than that. Due to the way fare pricing works, regional flights attached to long-hauls are often close to free, occasionally even cheaper than a flight terminating at the hub.
For trips where you only want to upgrade a few segments, buying the whole trip in economy and using miles to upgrade can be very cost effective.