Alrighty, Psy to the rescure:
Sean wrote:I think you might have gotten it the opposite way around; isn't it that you don't use honorific language with people in your ingroup?
You use honorific language within the hierarchy of
your in-group, but when you are talking to an out-group, everyone in your in-group is lower in status than that of the out-group. In other words, you're polite to the boss of your company
within that company, but when you are talking to an outsider about your boss, you'll use humble language.
奥 seems strange to me. You might be better off with 私の妻(つま), or just 妻のカリシャーナです instead.
There is 家内(かない), but I don't know if that's really very PC to use?
奥 = doesn't work.
妻 = Good but PC
家内 = Good but not PC.
The polite form would be いんめちます
隠滅(いんめつ)します, isn't it? It's a compound word, you wouldn't need to change it itself.
Both you and bloritsch are looking waaay too hard at this. (as a matter of interest, it would be 隠滅します) Step back and take a breath, notice the context. Does 何名様 fit the situation a little better? Anyways, back to the original question:
Answer however you like.
Answer both ways if you feel like it. You're not gonna offend anyone. You could say "二人です," to which you can add 私と家内の「名前」(だけ)です。 If you get a curious look in response, you'll know that you've answered in an unusual way for Japanese society. At any rate, from there you could talk about not having children, wanting children or waiting to have children-- all good topics of conversation. You could also talk about the family that raised you or how you met your wife, why you came to Japan, etc... don't obsess over the details. You'll make a cultural faux-pas eventually, so just do your best, analyze, correct and adapt where you can.
Don't forget to have fun, too.