Semiquantum key distribution protocols are designed to allow two parties to establish a shared secret key, secure against an all-powerful adversary, even when one of the users is restricted to measuring and preparing quantum states in one single basis. While interesting from a theoretical standpoint, these protocols have the disadvantage that a two-way quantum communication channel is necessary which generally limits their theoretical efficiency and noise tolerance. In this paper, we construct a semiquantum key distribution (SQKD) protocol which actually takes advantage of this necessary two-way channel, and, after performing an information theoretic security analysis against collective attacks, we show it is able to tolerate a channel noise level higher than any prior SQKD protocol to date. We also compare the noise tolerance of our protocol to other two-way fully quantum protocols, along with BB84 with classical advantage distillation. We also comment on some practical issues involving semiquantum key distribution (in particular, concerning the potential complexity in physical implementation of our protocol as compared with other standard QKD protocols). Finally, we develop techniques that can be applied to the security analysis of other (S)QKD protocols reliant on a two-way quantum communication channel.