I have done this the other way around. Bought my ticket from LAN, SCL-JFK-SFO (Don't ask why) with the JFK-SFO in JetBlue. They tagged my bags all the way through, but since I still had to go through customs, I had to pull it myself all the way to T5.
I bought this ticket from a LAN office, but they didn't actually knew they had an interline with B6 (I had to lecture them on it).
There is no codeshare and no miles/points/kilometers to be accrued on the other carrier, though, but you can buy your tickets (at least with LAN) and interline your bags at least LA->B6.
Did you try manually entering the airport code when you tried with LAN's website? Try, say a JFK-SCL and then look closely at the web address. Replace all "NYC" with your airport code and you might as well find it.
Good luck!!