A microwave photonic link (MPL) with simultaneous suppression of the even-order and third-order distortions using a polarization modulator (PolM), an optical bandpass filter (OBPF), and a balanced photodetector (BPD) is proposed and experimentally demonstrated. The even-order distortions are suppressed by utilizing orthogonal polarization modulation based on the PolM and balanced differential detection based on the BPD. The third-order distortions (IMD3) are suppressed by optimizing the spectral response of the OBPF with an optimal power ratio between the optical carrier and the sidebands of the phase-modulated signals from the PolM. Since the suppression of the IMD3 is achieved when the MPL is optimized for even-order distortion suppression, the proposed MPL can operate with simultaneous suppression of the even-order and third-order distortions. The proposed MPL is analyzed theoretically and is verified by an experiment. For a two-tone RF signal of f_1 = 10 GHz and f_2 = 19.95 GHz, the spurious-free dynamic range (SFDR2) is enhanced by 23.4 dB for the second harmonic (2f_1), and 29.1 and 27.6 dB for the second intermodulation (f_2-f_1 and f_1 + f_2), as compared with a conventional MPL. For a two-tone RF signal of f_1 = 9.95 GHz and f_2 = 10 GHz, the SFDR3 is increased by 13.1 dB as compared with a conventional MPL.