Is it wrong for two partners in a relationship to mutually agree that both partners will avoid members of the opposite sex who are not their partner? No, not necessarily. There's nothing wrong or even particularly damaging with the proposition alone so long as both parties agree upon the terms and conditions and refrain from violating said agreed upon terms.

It's the underlying insecurities that are bound to cause problems. And this particular arrangement is a result of those feelings. If you want to face the insecurities, the depression, and the mistrust, you need to address this issue.

Furthermore ... I'm assuming you're in high school or college (correct me if I'm wrong). It might be easier to avoid members of the opposite sex in such situations. But what will happen when one of you is forced to work alongside a member of the opposite sex? Be that for a work-related or school project. How are you going to react? How is he going to react?

It's great that he's understanding enough to help you through these problems. But is his behaviour really helping you or the relationship? Or, by reassuring you, is he reinforcing these negative behaviours of seeking validation when you feel insecure?

Are you happy?