This paper presents an interferometric synthetic aperture radar (InSAR) imaging method based on L<sub>1</sub> regularization reconstruction model for SAR complex-image and raw data via complex approximated message passing (CAMP) with joint reconstruction model. As an iterative recovery algorithm for L1 regularization, CAMP can not only obtain the sparse estimation of considered scene as other regularization recovery algorithms, but also a non-sparse solution with preserved background information, thus can be used to InSAR processing. The contributions of the proposed method are as follows. On the one hand, as multiple SAR complex images are strongly correlated, single-channel independent reconstruction via Lq regularization cannot preserve the interferometric phase information, while the proposed mixed norm-based L<sub>1</sub> regularization joint reconstruction model via CAMP algorithm can ensure the preservation of interferometric phase information among multiple channels. On the other hand, the interferogram reconstructed by the proposed CAMP-based InSAR imaging with joint reconstruction model can improve the performance of noise reduction efficiently compared with conventional matched filtering (MF) results. Experiments carried out on simulated and real data confirmed the feasibility of the L<sub>1</sub> regularization joint reconstruction model via CAMP for InSAR processing with preserved interferometric phase information and better noise reduction performance.