As a short answer they are interchangeable, specially in the literal use of the language when telling the colour of white.
For example: λευκά/άσπρα ρούχα.
But in some cases, mostly in the figurative use of the language, there are some set phrases where you can use only άσπρο or only λευκό. For example: Λευκός Οίκος (=White House); λευκή κόλλα (a test paper on which the student hasn't answered any question); λευκό ποινικό μητρώο (clean criminal record); λευκή περιστερά (=white fem. dove meaning pure/uncorrupted person) etc.
Also, the compounds ασπρομάλλης (=the man who has white hair) and ασπρόμαυρος (white+black). The phrases άσπρη μέρα -->lit. "white day", which means "happy day" and άσπρος σαν το γάλα = white like the milk.
If you want to generalize λευκό is used much more than άσπρο in the figurative use of "white" i.e. when you want to convey the meaning of "innocent", "clean", "clear" or "immaculate".
For the color white on the other side, I'd say that they are interchangeable with άσπρο having the advantage as it is a more colloquial and lay term while λευκό is more formal and literary.
I'd like to add that when buying clothes, underwear or fabrics in a store, λευkό is practically always used. 'Αυτό το φόρεμα υπάρχει σε μαύρο και σε λευκό'. Λευκά είδη means 'household fabrics' (sheets,towels,table linen).