The Interlock Protocol was described[1] as a method to expose a middle-man who might try to compromise two parties that use anonymous key agreement to secure their conversation.
Davies and Price proposed the use of the Interlock Protocol for authentication in a book titled Security for Computer Networks.
MITM can be attempted using the attack described in the Bellovin paper (Z being the man-in-the-middle): In this case, A receives the data approximately after 3*T, since Z has to perform the interlocking exchange with B.
Of course, Z could choose to not perform the Interlock Protocol with B (opting to instead send his own Mb) but then the session would be between A and Z, not A, Z, and B: Z wouldn't be in the middle.
For this reason, the interlock protocol cannot be effectively used to provide authentication, although it can ensure that no third party can modify the messages in transit without detection.