A balanced optical microwave phase detector (BOMPD) based on a 3×3 coupler is presented. This system was developed to extract ultra-low-jitter microwave signals from optical pulse trains emitted by mode-locked Er-fiber lasers, and synchronized microwave and laser systems. We demonstrate that the BOMPD achieves a precision of synchronization of less than 100 femtosecond of timing jitter. The experimental setup can be applied to the soft X-ray free-electron laser located on the campus of the Shanghai synchrotron radiation facility. A microwave signal with a 2.856 GHz frequency is extracted from a 238 MHz mode-locked Er-laser, with an absolute timing jitter of 34 fs in the 10 Hz-10 MHz frequency offset range. In addition, the microwave and 238 MHz optical pulse signals are synchronized with a relative timing jitter of 16 fs at the same frequency offset range.