So, I can't for the life of me figure out how to make this booking:

CPH to JFK via LHR, business class
LAX to CPH via LHR, economy

Can this be booked online?

If I want to be in the same cabin for both legs, no prob. Or if I want to fly to NYC from CPH in business and return from NYC in economy, no prob. But flying to one city in business, and back from a different in economy seems impossible to book online.

If I look for two one way flights the price is astronomical as opposed to the "real" price of a return flight to the US from CPH.

Any ideas? I looked at BA, Momondo, ITA Matrix and Kayak and all of them only allow you to select one cabin for the whole multi city search, not letting you select a cabin type per leg.