The sentence can have either meaning, his/hers or yours. You have to know from the context whom the speaker means. If you speak to someone in the polite form (lei and third person verb forms), then you have to go whole hog and use the reflexive pronoun si and the possessive suo.
I think "panino" is usually used to mean sandwich, although literally it means "little bread" (as in, a roll instead of a loaf). In fact, you see it now in American restaurants that have a special grill to make Italian-style sandwiches --except they always say "panini" for one sandwich, which drives me crazy!