We fabricate a membrane InP-based electroabsorption modulator (EAM), in which an InGaAsP-based multiple-quantum-well (MQW) absorption region is buried with an InP layer, on Si-waveguide circuits. By optical coupling between the MQW absorption region and Si core, a low-loss and large-absorption-length (300-m-long) supermode waveguide is designed to suppress electric-field screening at high optical input power. The EAM is fabricated by combining direct bonding of the MQW layer and regrowth of the InP layer on a thin InP template bonded on a silicon-on-insulator wafer. The fabricated membrane EAM shows an on-chip loss of less than 4 dB at wavelengths over 1590 nm and temperatures from 25 to 50°C. Since the membrane lateral p-i-n diode structure is beneficial for reducing the RC time constant of a lumped-electrode InP-based EAM, the EO bandwidth of the EAM is around 50 GHz without a 50-ohm termination up to fiber-input power of 10 dBm. Using the device, we demonstrate clear eye openings for 56-Gbit/s NRZ and 112-Gbit/s PAM4 signals at temperatures from 25 to 50°C.