Neural networks have shown great potential in language modeling. Currently, the dominant approach to language modeling is based on recurrent neural networks (RNNs) and convolutional neural networks (CNNs). Nonetheless, it is not clear why RNNs and CNNs are suitable for the language modeling task since these neural models are lack of interpretability. The goal of this paper is to tailor an interpretable neural model as an alternative to RNNs and CNNs for the language modeling task. This paper proposes a unified framework for language modeling, which can partly interpret the rationales behind existing language models (LMs). Based on the proposed framework, an interpretable neural language model (INLM) is proposed, including a tailored architectural structure and a tailored learning method for the language modeling task. The proposed INLM can be approximated as a parameterized auto-regressive moving average model and provides interpretability in two aspects: component interpretability and prediction interpretability. Experiments demonstrate that the proposed INLM outperforms some typical neural LMs on several language modeling datasets and on the switchboard speech recognition task. Further experiments also show that the proposed INLM is competitive with the state-of-the-art long short-term memory LMs on the Penn Treebank and WikiText-2 datasets.