Yes, it should provide the information that both parties gave about their respective parents, as well as information about themselves, and it should also give names of the witnesses.
Add, I should note that the above refers to the info I find on several NZ bdm PRINTOUTS I understand printouts are more detailed than the actual certificate. There's also ITMs that can be searched too, and there's some great NZ RChatters.
Cheers, JM