As an English speaker, I've never heard "disappointed with" used with the same meaning as "disappointed in". To me, "disappointed with" would mean the same thing as the Dutch "teleurgesteld met". It's also used with non-animate nouns such as "I'm disappointed with this project I'm working on."
I'm guessing the Dutch "Ik ben teleurgesteld in je" is something a parent might say to a child for getting bad grades in school or for getting into trouble. If so, then the English equivalent is definitely "I'm disappointed in you."
You can say both, though to a native English speaker the connotations are different. "by" makes it more impersonal, and is more often used with something (even though it can be used with some one). "In" makes it much more personal, and expresses more of a feeling of being let down.