Image Salient Object Detection (SOD) is a fundamental research topic in the area of computer vision. Recently, the multimodal information in RGB, Depth (D), and Thermal (T) modalities has been proven to be beneficial to the SOD. However, existing methods are only designed for RGB-D or RGB-T SOD, which may limit the utilization in various modalities, or just finetuned on specific datasets, which may bring about extra computation overhead. These defects can hinder the practical deployment of SOD in real-world applications. In this paper, we propose an end-to-end Unified Triplet Decoder Network, dubbed UTDNet, for both RGB-T and RGB-D SOD tasks. The intractable challenges for the unified multimodal SOD are mainly two-fold, i.e., (1) accurately detecting and segmenting salient objects, and (2) preferably via a single network that fits both RGB-T and RGB-D SOD. First, to deal with the former challenge, we propose the multi-scale feature extraction unit to enrich the discriminative contextual information, and the efficient fusion module to explore cross-modality complementary information. Then, the multimodal features are fed to the triplet decoder, where the hierarchical deep supervision loss further enable the network to capture distinctive saliency cues. Second, as to the latter challenge, we propose a simple yet effective continual learning method to unify multimodal SOD. Concretely, we sequentially train multimodal SOD tasks by applying Elastic Weight Consolidation (EWC) regularization with the hierarchical loss function to avoid catastrophic forgetting without inducing more parameters. Critically, the triplet decoder separates task-specific and task-invariant information, making the network easily adaptable to multimodal SOD tasks. Extensive comparisons with 26 recently proposed RGB-T and RGB-D SOD methods demonstrate the superiority of the proposed UTDNet.