Understanding fundamental limits of the anti-interference performance of direct sequence spread spectrum (DSSS) systems is essential for efficient anti-interference implementation. Existing research contributions on anti-interference implementation mainly aims at blocking interference and DSSS with long period sequences (LPS-DSSS). However, broadband interference, due to high energy efficiency, is a more effective interference mode to DSSS systems. Conventional bit error rate (BER) models bring errors during the despreading process in DSSS with short period sequences (SPS-DSSS). Therefore, in this paper, we propose the maximum matching decision criteria (MMDC) based statistical BER model that is capable of accurately evaluating the BER for both LPS and SPS systems. Firstly, explicit mathematical model of the despreading of MSK signals in DSSS systems is established; Then, mathematical models of despreading under typical interference modes, i.e., multi-tone and pseudo-random noise (PN) code MSK interference, are derived. Finally, statistical BER model is proposed using the MMDC scheme to evaluate the BER performance. Extensive simulation and experimental results reveal that: 1) the proposed statistic BER model outperforms conventional BER model for SPS-DSSS systems, and is consistence with that for LPS-DSSS; 2) for MSK DSSS systems, PN code MSK interference outperforms multi-tone interference in the BER performance; 3) practical tests demonstrate that the same PN code length interference is capable of obtaining higher BER performance than different PN code lengths interference, due to the strong correlation between the interference signal and the desired signal in DSSS systems.