How do I automatically insert a row into parent table when a row is created in a child table?

Question

I am working on a MySQL database that has to treat organizations and people as interchangeable in some instances and not others. Because of this, I created a table called LegalEntity as a superclass. It has an optional 1 to 1 relationship with two other tables: Person and Organization. How I can make the database automatically insert a row into LegalEntity whenever I insert a new row into Person or Organization?