The Church refers to families with children who do not live with their own mother and father united in marriage as irregular family situations. Following the Church's lead, we can refer to united families (that some describe as "traditional") as "regular families."
Why do we advocate for "regular families" rather than "natural families" in reintroducing marriage reality?"
Regular is a good word to use, because it conveys the norm that we are seeking to restore, i.e. the norm of men and women choosing to make themselves irreplaceable to each other through marriage in preparation for receiving children as a gift.
Regular family describes the situation of a united family. It is regular for a child to be united with their mother and father and irregular to be separated by illness, death, divorce or intentional privation through donor or surrogate conception. The situation of children deprived of their mother and father can possibly be regularized if adopted by a married man and woman.
Using the term "natural family" gets a bit confusing. It is natural and common* that each and therefore everyone without exception has their own mother and father. We know from scripture that it is God's plan for man and woman to become related to each other (one flesh) and multiply in that state. We can verify God's plan through our own experience (common because it is stamped in our nature by God) of our desire to know where we came from and to be united and loved by our own mother and father and extended family.
Although there is a human inclination toward marriage reality, it in and of itself is not really natural. Entering into marriage is a matter of the will, a choice of man and woman to make themselves irreplaceable (kin) to each other, which is obviously irrevocable.
* The use of "common" is in the context of Church teaching related to the principle of the "common good" ("Common" defined as pertaining to each and therefore to every person without exception, and "good" that which promotes human flourishing. Ones own mother and father are common goods.