Due to its high precision, phase-shifting interferometry (PSI) is a commonly used optical component detection method in interferometers. However, traditional PSI, which is susceptible to environmental factors, is costly, with piezoelectric ceramic transducer (PZT) being a major contributor to the high cost of interferometers. In contrast, two-frame random interferometry does not require precise multiple phase shifts, which only needs one random phase shift, reducing control costs and time requirements, as well as mitigating the impact of environmental factors (mechanical vibrations and air turbulence) when acquiring multiple interferograms. A novel method for wavefront reconstruction using two-frame random interferometry based on Swin-Unet is proposed. Besides, improvements have been made on the basis of the established algorithm to develop a new wavefront reconstruction method named Phase U-Net plus (PUN+). According to training the Swin-Unet and PUN+ with a large amount of simulated data generated by physical models, both of the methods accurately compute the wrapped phase from two frames of interferograms with an unknown phase step (except for multiples of pi). The superior performance of both methods is effectively showcased by reconstructing phases from both simulated and real interferograms, in comprehensive comparisons with several classical algorithms. The proposed Swin-Unet outperforms PUN+ in reconstructing the wrapped phase and unwrapped phase.