William of Orange was not a member of the house of Stuart - he was simply married to a member of that house. (And even if he were a member of the house, I don't really see why that's relevant to the question whether what he did was an invasion and occupation.) More importantly, he was not invited to invade by parliament. Some MPs, acting on their own initiative as private individuals, invited him to invade. That was not a formal invitation by parliament. Once they'd done it, parliament basically said, "We would like to be the first to welcome our new Dutch overlords," but parliament did not initiate the event.
The fact that some people invited the invasion doesn't stop it from being an invasion. If, during WWII, Oswald Mosley had written to Hitler inviting him to invade Britain and it had happened, it would still have been an invasion.
William didn't just turn up on the ferry from Ostend and walk into London unopposed. He had a great big army standing right behind him. In the event, there was no fighting, because James II decided to run rather than fight (probably wisely). But if William hadn't had that army, he wouldn't have got past James and his army. What I'm saying is, he needed the army to succeed in the endeavour. I'd say that makes it an invasion. You can say it was a benevolent invasion, a welcome invasion, and a bloodless invasion (apart from James' nosebleed), and you may be right. But it's still an invasion, and moreover a foreign one.
Obviously there are other occasions when Britain was invaded and "occupied" even after 1066. The one that springs to mind is the invasion of Henry Bolingbroke in 1399, who also landed in the country with an army and displaced the king (in his case, forcing him to abdicate and then probably having him murdered). Of course that's not exactly a "foreign" invasion since Henry was English, but he did invade from overseas.