We propose and demonstrate a Michelson interferometer modulator with integrated Bragg reflectors on a silicon-rich nitride-thin-film lithium niobate hybrid platform. High-reflectivity Bragg reflectors are placed at the ends of both arms, which double the electro-optic (E-O) interaction length and reduce the velocity mismatch between the microwave and optical wave. The presented Michelson interferometer modulator achieves a measured half-wave voltage length product as low as 1.06 V cm and high-speed modulation up to 70 Gbps. A 3-dB E-O bandwidth beyond 40 GHz is also achieved, which is, to the best of our knowledge, the highest modulation bandwidth of Michelson interferometer modulators.