Automated sleep stage scoring for mice is in high demand for sleep research, since manual scoring requires considerable human expertise and efforts. The existing automated scoring methods do not provide the scoring accuracy required for practical use. In addition, the performance of such methods has generally been evaluated using rather small-scale datasets, and their robustness against individual differences and noise has not been adequately verified. This research proposes a novel automated scoring method named "MC-SleepNet", which combines two types of deep neural networks. Then, we evaluate its performance using a large-scale dataset that contains 4,200 biological signal records of mice. The experimental results show that MC-SleepNet can automatically score sleep stages with an accuracy of 96.6% and kappa statistic of 0.94. In addition, we confirm that the scoring accuracy does not significantly decrease even if the target biological signals are noisy. These results suggest that MC-SleepNet is very robust against individual differences and noise. To the best of our knowledge, evaluations using such a large-scale dataset (containing 4,200 records) and high scoring accuracy (96.6%) have not been reported in previous related studies.