"The cat sleeps among the dogs."
Translation:Katten sover iblandt hundene.
As prepositions, they're synonymous in the meaning of being at a place in the middle of or surrounded by something. However, blandt can also be used to indicate that it is inside a set or group. The phrase blandt andet (abbreviated bl.a.) is very common and means among other things (example: "han er bl.a. forfatter"/"he is among other things an author"). Iblandt can also have the meaning "inside a set or group", but only as an adverb (example (from Den Danske Ordbog): "man støder kun på få skulpturer, men der er perler iblandt"/"you only come across few sculptures, but there are pearls among (them)").