To be fair, I don't know exactly how they interact. I know that INTERPOL has been recognized by the United Nations as an international organization. They do operate under international law, not unlike the United Nations, and they do work with the United Nations. One of the notices, in fact, is the INTERPOL-UN council special notice, which is issued for groups and individuals associated with al Qaeda or Taliban, and subject to sanctions and so on. They do work with different United Nations organizations, different subcommittees and so on, where there is a law enforcement interest.
On November 22nd, 2018. See this statement in context.