A broadband and CMOS-compatible polarization beam splitter and rotator (PSR) built on the silicon nitride-on-silicon multilayer platform is presented. The PSR is realized by cascading a polarization beam splitter and a polarization rotator, which are both subtly constructed with an asymmetrical directional coupler waveguide structure. The advantage of this device is that the function of PSR can be directly realized in the SiN layer, providing a promising solution to the polarization diversity schemes in SiN photonic circuits. The chip is expected to have high power handling capability as the light is input from the SiN waveguide. The use of silicon dioxide as the upper cladding of the device ensures its compatibility with the metal back-end-of-line process. By optimizing the structure parameters, a polarization conversion loss lower than 1 dB and cross talk larger than 27.6 dB can be obtained for TM-TE mode conversion over a wavelength range of 1450 to 1600 nm. For TE mode, the insertion loss is lower than 0.26 dB and cross talk is larger than 25.3 dB over the same wavelength range. The proposed device has good potential in diversifying the functionalities of the multilayer photonic chip with high integration density.