The phase noise of microwaves extracted from optical frequency combs is fundamentally limited by thermal and shot noise, which is inherent in photodetection. Saturation of a photodiode due to the high peak power of ultrashort optical pulses, however, prohibits further scaling of white phase noise by increasing incident optical power. Here we demonstrate that the photocurrent pulse shaping via balanced photodetection, which is accomplished by replacing a single photodiode with a balanced photodetector (BPD) and delaying one of the optical pulses, provides a simple and efficient optical-to-electrical interface to increase achievable microwave power and reduces the corresponding thermal noise-limited phase noise by 6-dB. By analysing contributing noise sources, we also show that the thermal noise floor can reach - 166 dBc/Hz even at a low photocurrent of 2-mA (4-mW optical input per photodiode) when using a p-i-n BPD. This finding may be useful for on-chip microwave generation, which consists of standard p-i-n structure photodiodes with relatively low saturation optical power.