Despite their alarm, and inability to escape without prying open the plane's hatch, the couple were evidently able to maintain their composure. They didn't squash the "scary" spider, or fling him out in a fit of panic, but rather kept him safe for the duration of the flight.
Upon landing in Munich, the couple informed airport staff of the arachnid, and customs officials then took custody of him from there. According to local media reports, a veterinarian confirmed the spider to be a huntsman spider — a pretty friendly and harmless species from Australia that can grow to have a leg span of about 7 inches.
Customs officials, thankfully, were sympathetic for the spider, too, and are said to be seeking a caretaker for him.