The segmentation of the ventricular wall and the blood pool in cardiac magnetic resonance imaging (MRI) has been investigated for decades, given its important role for delineation of cardiac functioning and diagnosis of heart diseases. One of the major challenges is that the inner epicardium boundary is not always visible in the image domain, due to the mixture of blood and muscle structures, especially at the end of contraction, or systole. To address it, we propose a novel approach for the cardiac segmentation in the short-axis (SAX) MRI: coupled deep neural networks and deformable models. First, a 2D U-Net is adopted for each magnetic resonance (MR) slice, and a 3D U-Net refines the segmentation results along the temporal dimension. Then, we propose a multi-component deformable model to extract accurate contours for both endo- and epicardium with global and local constraints. Finally, a partial blood classification is explored to estimate the presence of boundary pixels near the trabeculae and solid wall, and to avoid moving the endocardium boundary inward. Quantitative evaluation demonstrates the high accuracy, robustness, and efficiency of our approach for the slices acquired at different locations and different cardiac phases.