The daughter of Ayrs and Jocasta, Eva is, as Frobisher observes, "the crowning glory of six centuries' breeding" (2.2.9). This is a pretty apt description, seeing how Ayrs and Jocasta view people as property anyway. They may as well consider their daughter to be a prize horse.
Although Frobisher dislikes Eva at first, getting into vicious French-language spats with her saying "her hobbies are pouting and looking martyred" (2.3.17), he eventually realizes that he's in love with her. Unfortunately, due to a misunderstanding of Three's Company proportions (but without the humor), Frobisher mistakenly believes that Eva is in love with him, too.
Eva reveals something about Frobisher to us. Frobisher says: "the devious vixen is almost a female Me" (2.5.9). Later, he reveals, "I've never loved anyone except myself" (2.9.3). No wonder he loves her so much; she has all the same qualities he does—boyish good looks, killer wit, and a feisty personality. Shame it didn't work out.