The parity symmetry of the cosmic microwave background (CMB) pattern as seen by Wilkinson Microwave Anisotropy Probe 7 yr (WMAP 7 yr) is tested jointly in temperature and polarization at large angular scale. A quadratic maximum likelihood (QML) estimator is applied to the WMAP 7-yr low-resolution maps to compute all polarized CMB angular power spectra. The analysis is supported by 10 000 realistic Monte Carlo realizations. We confirm the previously reported parity anomaly for TT in the range δℓ=[2, 22] at >99.5 per cent C.L. No anomalies have been detected in TT for a wider ℓ range (up to ℓmax= 40). No violations have been found for EE, TE and BB which we test here for the first time. The cross-spectra TB and EB are found to be consistent with zero. We also forecast Planck capabilities in probing parity violations on low-resolution maps.