I work on boats. (Or at least I did before the depression killed the business.) What you want is "Structural Foam Core". For best results, it will need to adhered (glued) to both surface pieces. If I were doing it for strength, I would use end-grain balsa, but just a door does not need that much strength. If you want the door to be real ridgid, you need a high density. If you don't need it that stiff, don't buy it. This is different stuff than insulating board at a big box, but not a lot different.
Matt
