No, the Green Hornet isn't part of Marvel or DC Comics. It has its unique comic book history and storyline that's distinct from both of those major comic publishers.
First, you need to understand the basic concepts of both Marvel and Green Lantern universes. For your OC (Original Character), think about their unique power set. Maybe it could be a combination of a Green Lantern's power ring abilities and a Marvel - like superpower, like Wolverine's healing factor. Design their backstory carefully, for example, they could be from a planet that has a connection to both universes.