Identification of autism spectrum disorder (ASD) in children is challenging due to the complexity and heterogeneity of ASD. Currently, most existing methods mainly rely on a single modality with limited information and often cannot achieve satisfactory performance. To address this issue, this paper investigates from internal neurophysiological and external behavior perspectives simultaneously and proposes a new multimodal diagnosis framework for identifying ASD in children with fusion of electroencephalogram (EEG) and eye-tracking (ET) data. Specifically, we designed a two-step multimodal feature learning and fusion model based on a typical deep learning algorithm, stacked denoising autoencoder (SDAE). In the first step, two SDAE models are designed for feature learning for EEG and ET modality, respectively. Then, a third SDAE model in the second step is designed to perform multimodal fusion with learned EEG and ET features in a concatenated way. Our designed multimodal identification model can automatically capture correlations and complementarity from behavior modality and neurophysiological modality in a latent feature space, and generate informative feature representations with better discriminability and generalization for enhanced identification performance. We collected a multimodal dataset containing 40 ASD children and 50 typically developing (TD) children to evaluate our proposed method. Experimental results showed that our proposed method achieved superior performance compared with two unimodal methods and a simple feature-level fusion method, which has promising potential to provide an objective and accurate diagnosis to assist clinicians.