[kqbx]

Sounds like you're describing a three-pass protocol: https://en.wikipedia.org/wiki/Three-pass_protocol

Note that this requires the encryption to be commutative - in the third step Alice has a message in the form e_B(e_A(msg)), where e_B and e_A are Bob's and Alice's encryption functions. Alice must be able to apply her key to obtain e_B(msg), removing the inner encryption. This can be achieved with some modular exponentiation magic.

I don't know of any practical applications of this, probably because it requires both parties to be online at the same time, so they may as well use the simpler Diffie-Hellman key exchange.