Reliable estimation of vehicle lateral position plays an essential role in enhancing the safety of autonomous vehicles. However, it remains a challenging problem due to the frequently occurred road occlusion and the unreliability of employed reference objects (e.g., lane markings, curbs, etc.). Most existing works can only solve part of the problem, resulting in unsatisfactory performance. This paper proposes a novel deep inference network (DINet) to estimate vehicle lateral position, which can adequately address the challenges. DINet integrates three deep neural network (DNN)-based components in a human-like manner. A road area detection and occluding object segmentation (RADOOS) model focuses on detecting road areas and segmenting occluding objects on the road. A road area reconstruction (RAR) model tries to reconstruct the corrupted road area to a complete one as realistic as possible, by inferring missing road regions conditioned on the occluding objects segmented before. A lateral position estimator (LPE) model estimates the position from the reconstructed road area. To verify the effectiveness of DINet, road-test experiments were carried out in the scenarios with different degrees of occlusion. The experimental results demonstrate that DINet can obtain reliable and accurate (centimeter-level) lateral position even in severe road occlusion.