Delta-Differential One-Way Ranging (DeltaDOR) is widely used in deep spacecraft navigation, and cross support could enhance navigation accuracy with more interferometry baselines and longer baseline. In China Mars mission Tianwen-1, formal joint cross-support interferometry tracking between China Satellite Launch and TT&C General (CLTC) and European Space Operations Center (ESOC) under commercial contract was conducted around the critical stages of the mission, such as Mars orbit insertion. Cross-support interferometry is a new challenge to CLTC, as the correlator for routine DeltaDOR measurements do not fit for cross support, because of observable definition, blind station clock searching, and so on. This paper discusses the new method and algorithm adopted in joint cross support, especially for spacecraft tone signal processing and clock estimation when correlating with the data of two stations from different agencies. Results of the cross-support interferometry tracking activities are also analyzed. Observables from CLTC and ESOC are consistent with each other, and the difference in observables is in the order of tens of ps. All the baselines are induced to evaluate the accuracy of the spacecraft orbit determined and predicted by CLTC, and the DeltaDOR residuals have a root-mean-square (RMS) better than 0.5 ns (the goal is 1 ns), which could enhance the confidence of the orbit accuracy and the effectiveness of control parameters during critical orbit operation.