It is was possible for Cupid and Psyche to be married because Psyche was become immortal by eating ambrosia seeking to be with Cupid.
Since Zeus realized that Eros, who is also refered to as Cupid, was miserable without Psyche (who was a human), he made Psyche immortal by granting her the wish to turn into a goddess. so that they could be married. Cupid had retrieved her from the underworld which made this possible.