This paper proposes methods for reconstructing the short-time Fourier transform phase from the amplitude using deep neural networks (DNNs). When only the amplitude is available, the phase reconstruction is affected by a sign indetermination problem in which the amplitude cannot specify the sign for the signal; therefore, there are at least two phases verifying an amplitude, corresponding to the original signal and its negation. This problem may affect the DNN training process as the same inputs yield very different loss values. In this paper, we address the sign indetermination problem for the DNN-based phase reconstruction. More specifically, we propose a phase loss function derived from a von Mises mixture model, which is used to model the phases of both original signal and its negation. We also enhance the consistency between phase elements by penalizing the errors of phase derivatives, i.e., instantaneous frequency and group delay. The experimental results show that the proposed methods outperform conventional methods in terms of the quality of the reconstructed signals and consistency between the estimated phase and amplitude.