The Air NZ website doesn't seem that clear on what happens when your journey is on one ticket spanning different airlines:

"Please note that if your itinerary involves Air New Zealand flights where both the 'piece' and 'weight' baggage allowances apply, we will extend the more generous 'piece' allowance to all Air New Zealand flights on that same ticketed itinerary. If your itinerary also involves flights operated by another airline/s, please refer directly to them for their allowance."

http://www.airnewzealand.co.nz/checked-in-baggage

I remember digging out for another poster recently an excerpt from the website which said that Air NZ would extend the highest baggage allowance for any one NZ flight to all other NZ flights on the same ticket, but I can't seem to find the link again. If this holds true, however, then at the minimum the OP would be entitled to 2 pieces per person (2 pieces being the allowance for TT J), unless any of his party is *G in which case they will get +1.

TK - I might be woefully off base here, but weren't NZ actually correct? As my understanding goes, when connecting on a different airline, whether on the same ticket or not, the baggage allowance of the first airline applies. This is why (for example) when I fly JFK-LAX-AKL in J on UA/NZ, United will only let me check 2 bags even though in the reverse direction I would be able to check 3.