AP and AD is rarely an effective combination.
The champs most likely to make this work:
An AP centric build with Blade of the Ruined King
can probably work pretty well as a mixed auto attacker.
A harder to use skirmish/burst caster assassin. She has mixed scalings. Is better with a full AP or AP focused build. Triforce
is probably her best AD item.
Has hybrid scalings. Typically built as an AD bruiser/tank. If you're really fed hybrid can work. To be honest a hybrid build is too expensive to get early or leaves him too squishy late game. Still a good mention because even if you build Jax his standard build (Triforce/Blade of the Ruined King into tank items) he'll still do good mixed damage. He is supposed to be a hyper carry fighter type (weaker early game)
You can play a lot of champs hybrid but those are probably the most viable ones.