Roadrunner, the answer is that she is homeschooled and her material is associated with a private school. You then list each course and assign the appropriate provider for that course (AP Chemistry, PA Homeschoolers.....AP Bio, CTY.....etc). So there is a way to show that the kid is homeschooled but associated with a private school that will issue a diploma, and also associate each course with the appropriate provider.
EKS, it is considered homeschooling the exact same way that, well, homeschooling is homeschooling. For example, D21 took courses through all different providers (CTY Online, PA Homeschoolers, two different colleges, a few other providers) plus she had courses at home that were homemade. All decisions on coursework and providers etc were made by our family, we then let Clonlara know what D21 was doing. Clonlara is great - they are as hands-off or as hands-on as you ask them to be, and they offer suggestions and guidance when asked. We used Clonlara to put everything into one transcript, and the homemade courses are considered Clonlara credits under their Off-Campus program. So the education is exactly the same, just that instead of or in addition to the homeschooling transcript, Clonlara issues a transcript. The advantage with the Clonlara transcript is that Clonlara is an accredited private school. So during college application season, the kid can apply either as a homeschooled student or a private school student. My D21 applied as a homeschooled student through the Common App with a note that her homeschool program had oversight through Clonlara. Of course, homeschoolers don't NEED oversight from accredited schools, but due to personal circumstances (health reasons), I wanted D21 to have that extra insurance in case something happened to me before she graduated. Clonlara would have helped her put everything together and made it a bit easier for her to transfer into a public or private high school with the homeschooled credits she had already earned.