Here's how it all went for me back in June:

MEL-SYD-LAX-ANC: Arrived at TBIT on DL, cleared immigration, claimed luggage, cleared customs, dropped luggage off at the transfer desk, went outside and walked along arrivals road to Alaska's terminal (T6 I think from memory), cleared security, boarded aircraft.

YVR-LAX-SYD-MEL: Luggage checked through to MEL
Arrived on Air Canada at T2, caught bus around to DL's T5, entered the Delta One kerbside 'lounge'; had an orange juice as it was hot, cleared security, entered DL's lounge and drank beer and other alcoholic beverages for a few hours, boarded plane to Sydney. No dramas except for DL's late boarding and departure.