Denoising and demosaicking long-wave infrared (LWIR) division-of-focal-plane (DoFP) polarization images are crucial for various vision applications. However, existing methods rely on the sequential application of individual denoising and demosaicking processes, which may result in the accumulation of errors produced by each process. To address this issue, we propose a joint denoising and demosaicking method for LWIR DoFP images based on a three-stage progressive deep convolutional neural network. To ensure the generalization ability of this network, it is essential to have adequate training data that closely resembles real data. Therefore, we model the complex noise sources that affect LWIR DoFP images as mixed Poisson-Additive-Stripe noise and construct a least-squares problem based on the polarization measurement redundancy error to estimate the parameters of this model on real images. Subsequently, the estimated noise parameters are used to generate training data that enables the network to learn accurate polarization image statistics and improve its generalization ability. The experimental results demonstrate the effectiveness of the proposed method in enhancing the image restoration performance on real LWIR DoFP polarization data.