Booking in multiple classes
 

This isn't directly related to accumulating mileage but haven't found any information related to it elsewhere:

Which airlines allow booking roundtrip in multiple classes?
ex: LX allows me to book my overnight JFK-GVA in P (business) and the daytime GVA-JFK in T (economy).

I've found that I can assemble this type of itinerary on Swiss and United websites and imagine that other carriers must allow it also. Would one have to call and make a booking to combine seat classes?

There are some airlines where it can be booked through their website directly. Others you would need to call or use a TA. However sometimes discount economy/business fares cannot be combined so it can actually cost more than discount business return.

Are you paying for flts or using miles?

Assuming cash so we'll try the TB! forum.