- How are the wife and kid?
- How is the wife and kid?
Which is more correct?
"Are" is correct for most compound subjects, except for singular meanings (i.e. mac and cheese is) and alternative subjects (you or your wife is -- you or your friends are, though -- matches subject closest to the verb). Yay for style manuals.
It's not a question of "more" correct. The first (using "are") is correct, and the second (using "is") is not.
As others have mentioned, you shouldn't say "How is the wife and kid(s)." It's neither idiomatic, nor generally considered grammatical in standard English.
"How are the wife and kid(s)" would be considered grammatical, for the reasons Gamileon gave (compound subjects are generally treated as plural).
The most idiomatic way of saying this, though, is "How's the wife and kid(s)" with the contraction "How's". Unlike "How is", "How's" is commonly used with a plural subject. Pedants may call this ungrammatical, but it's a well-established feature of English idiom, and since this expression is fairly idiomatic and colloquial I don't think it's a problem if you use idiomatic but nonstandard grammar.
Check out this chart from the Google Ngram Viewer:
For more information on structures like "How's" with a plural subject, see my answer to the following question: Use of "Here's" before a plural noun
When in doubt, a useful test involves substituting pronouns. Consider
How is they?
How are they?
Say the wife and kid live in different places—maybe the latter is away at school—and you want to express this independence, you might use
How is the wife? The kid?
Any more explicit and the repetitiveness will be tiresome.
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