Dispersion engineering for efficient supercontinuum generation (SCG) is investigated in a hybrid nonlinear photonic platform that allows cascaded third- and second-order optical nonlinearities in transverse-electric (TE) guided modes. The highly nonlinear chalcogenide waveguides enable SCG spanning over 1.25 octaves (from about 1160 nm to more than 2800 nm at 20 dB below maximum power), while the TE polarization attained is compatible with efficient second-harmonic generation in a subsequent thin-film lithium niobate waveguide integrated monolithically on the same chip. A low-energy pump pulsed laser source of only 25 pJ with 250 fs duration, centered at a wavelength of 1550 nm, can achieve such wideband SCG. The design presented is suitable for the f-to-2f carrier-envelope offset detection technique of stabilized optical frequency comb sources.