The emergence of deep learning methods that complement traditional model-based methods has helped achieve a new state-of-the-art for image dehazing. Many recent methods design deep networks that either estimate the haze-free image (J) directly or estimate physical parameters in the haze model, i.e. ambient light (A) and transmission map (t) followed by using the inverse of the haze model to estimate the dehazed image. However, both kinds of methods fail in dealing with non-homogeneous haze images where some parts of the image are covered with denser haze and the other parts with shallower haze. In this work, we develop a novel neural network architecture that can take benefits of the aforementioned two kinds of dehazed images simultaneously by estimating a new quantity - a spatially varying weight map (w). w can then be used to combine the directly estimated J and the results obtained by the inverse model. In our work, we utilize a shared DenseNet-based encoder, and four distinct DenseNet-based decoders that estimate J, A, t, and w jointly. A channel attention structure is added to facilitate the generation of distinct feature maps of different decoders. Furthermore, we propose a novel dilation inception module in the architecture to utilize the non-local features to make up the missing information during the learning process. Experiments performed on challenging benchmark datasets of NTIRE'20 and NTIRE'18 demonstrate that the proposed method -namely, AtJwD- can outperform many state-of-the-art alternatives in the sense of quality metrics such as SSIM, especially in recovering images under non-homogeneous haze.