Abstract: We evaluate the polarization observables I-S and I-C for the reaction gamma p -> pi(0)eta p, using a chiral unitary framework developed earlier. The I-S and I-C observables have been recently measured for the first time by the CBELSA/TAPS Collaboration. The theoretical predictions of I-S and I-C, given for altogether 18 angle-dependent functions, are in good agreement with the measurements. Also, the asymmetry d Sigma/dcos theta evaluated here agrees with the data. We show the importance of the Delta(1700) D-33-resonance and its S-wave decay into eta Delta(1232). The result can be considered as a further confirmation of the dynamical nature of this resonance. At the highest energies, deviations of the predictions from the data start to become noticeable, which leaves room for additional processes and resonances such as a Delta(1940) D-33. We also point out how to further improve the calculation.