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Major depressive disorder (MDD) is one of the most common mental health disorders that can affect sleep, mood, appetite, and behavior of people. Multimodal neuroimaging data, such as functional and structural magnetic resonance imaging (MRI) scans, have been widely used in computer-aided detection of MDD. However, previous studies usually treat these two modalities separately, without considering their potentially complementary information. Even though a few studies propose integrating these two modalities, they usually suffer from significant inter-modality data heterogeneity. In this paper, we propose an adaptive multimodal neuroimage integration (AMNI) framework for automated MDD detection based on functional and structural MRIs. The AMNI framework consists of four major components: (1) a graph convolutional network to learn feature representations of functional connectivity networks derived from functional MRIs, (2) a convolutional neural network to learn features of T1-weighted structural MRIs, (3) a feature adaptation module to alleviate inter-modality difference, and (4) a feature fusion module to integrate feature representations extracted from two modalities for classification. To the best of our knowledge, this is among the first attempts to adaptively integrate functional and structural MRIs for neuroimaging-based MDD analysis by explicitly alleviating inter-modality heterogeneity. Extensive evaluations are performed on 533 subjects with resting-state functional MRI and T1-weighted MRI, with results suggesting the efficacy of the proposed method.