It is well known that for binary offset carrier (BOC) signals the notorious ambiguity problem due to the multipeaked autocorrelation function must be tackled first in order to obtain the potential of improving ranging performance promised by its broader Gabor bandwidth. The existence of multipath makes it more difficult to solve. Dual binary phase-shift keying (BPSK) tracking (DBT) is a kind of low complexity, unambiguous tracking method for BOC-family signals, which makes full use of the coherence between the upper and lower sidebands and employs subcarrier phase locked loop (SLL) and delay locked loop (DLL) to track subcarrier and code components, respectively. Considering that the thermal noise performance of DBT has been fully studied, this article focuses on the analysis of multipath performance and the design of antimultipath methods under DBT framework. The influence of multipath on SLL and DLL of DBT is analyzed first and the corresponding subcarrier and code multipath error envelopes are obtained. Then according to different requirements of subcarrier and code multipath errors, a multipath mitigation scheme specially designed for DBT is proposed, in which SLL and DLL adopt offset correlator and narrow correlation, respectively. Theoretical analysis and simulation are given to verify the effectiveness of the proposed methods.