my family

Either can be correct looking on the context, however "with family" (with no article) is most typically correct.

"Family" while not a piece of writing will sit down with any kind of relative and to the relatives of any variety of individuals.

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 would use "the family" only if you are referring to a specific family. For example:

My dad likes his job. Working from home results in more time to spend with the family.

In this case we actually do mean one specific family, that of the father and the child.

Note that during this context we are able to conjointly drop the article while not extremely dynamical the meaning:

My dad likes his job. Working from home results in more time to spend with family.

Without the article, we are again referring to family in general.

However, we tend to still perceive that we tend to ar talking regarding the precise family of the daddy and kid.

As such, dropping the article may be a safe selection in each things.