We present a heterogeneously coupled Si/SiO2/SiN waveguide structure that can achieve extremely high dispersions (> | ± 107| ps · nm-1km-1). A strong mode coupling between the Si and SiN waveguides introduces a normal dispersion to symmetric mode and an anomalous dispersion to anti-symmetric mode, and the large group velocity difference between the two waveguides results in such high dispersions. Geometric parameters of the structure control the peak dispersions and the central wavelength of the mode coupling, and these engineering capabilities are studied numerically. Analytical representations on the heterogeneously coupled waveguides are also introduced and these equations explain the effects of geometric parameters. This extremely dispersive waveguide scheme can be constructed with other material combinations as well and should be of interest in ultrafast signal processing and spectroscopic applications.