Dual-wavelength in-line digital holography (DIDH) is one of the popular methods for quantitative phase imaging of objects with non-contact and high-accuracy features. Two technical challenges in the reconstruction of these objects include suppressing the amplified noise and the twin-image that respectively originate from the phase difference and the phase-conjugated wavefronts. In contrast to the conventional methods, the deep learning network has become a powerful tool for estimating phase information in DIDH with the assistance of noise suppressing or twin-image removing ability. However, most of the current deep learning-based methods rely on supervised learning and training instances, thereby resulting in weakness when it comes to applying this training to practical imaging settings. In this paper, a new DIDH network (DIDH-Net) is proposed, which encapsulates the prior image information and the physical imaging process in an untrained deep neural network. The DIDH-Net can effectively suppress the amplified noise and the twin-image of the DIDH simultaneously by automatically adjusting the weights of the network. The obtained results demonstrate that the proposed method with robust phase reconstruction is well suited to improve the imaging performance of DIDH.