Electrical impedance tomography (EIT) is an emerging imaging modality to monitor 3D cell culture dynamics through reconstructing the electrical properties of cell clusters. Recently, machine-learning (ML)-based approaches have achieved significant gains for the image reconstruction of EIT against conventional physical model-based methods. However, continuous, multilevel conductivity distributions, which commonly exists in cell culture imaging, are more rigorous to reconstruct and remains challenging. This study aims to tackle this challenge by proposing a structure-aware dual-branch deep-learning method to predict both structure distribution and conductivity values. The proposed network comprises two independent branches to encode the structure and conductivity features, respectively. The two branches are jointed later to make final predictions of conductivity distributions. Numerical and experimental evaluation results demonstrate the superior performance of the proposed method in dealing with the multilevel, continuous conductivity reconstruction problem.