I've booked a few business fares through the portal on different star carriers - sometimes it can be great value, sometimes not... The portal should show every class that is available on star carriers + some partners - try booking a close in LH trip e.g. FRA to SIN next monday and you will see availability in Y/J/F (LH tends to release a lot of availability in all cabins just before departure). I find it's generally easier to search for star alliance availability using the United award search tool, the availability on there for star partners should be the same as Air NZ has access too even if the tool doesnt show them.