Yes. It's either Bilen min (definitive noun + possessive) or Min bil (possessive + indefinite noun).
Or Den grønne bilen min vs Min grønne bil (my green car). Det store huset mitt vs Mitt store hus (my big house). The adjective is always stuck in front of the noun, so it doesn't change it's place as such.
And as Luke_5.1991 says, if the possessive is in front of the noun if emphasises the possessor.