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Either could be correct depending on the context, but "with family" (with no article) is most generally correct. "Family" without an article can refer to any type of relative and to the relatives of any number of people. For example: Our employees like the new policy. Working from home results in more time to spend with family. Here we are talking about many families of many employees. If we said "the family" in the above context, we would be implying that all the employees are related, which is possible but unlikely. I