Do I use "is" or "are"?

Since there's a plural subject, there must be a plural verb. Are is correct.

To determine whether to use "is" or "are" in the sentence, we need to consider the subject of the sentence. In this case, the subject is "He and his family."

Since the subject "He and his family" is plural (referring to multiple people), we should use the plural form of the verb, which is "are."

Therefore, the correct sentence would be:

"He and his family are doing great."