Existing deep convolutional neural networks (CNNs) have recently achieved great success in pansharpening. However, most deep CNN-based pansharpening models are based on "black-box" architecture and require supervision, making these methods rely heavily on the ground-truth data and lose their interpretability for specific problems during network training. This study proposes a novel interpretable unsupervised end-to-end pansharpening network, called as IU2PNet, which explicitly encodes the well-studied pansharpening observation model into an unsupervised unrolling iterative adversarial network. Specifically, we first design a pansharpening model, whose iterative process can be computed by the half-quadratic splitting algorithm. Then, the iterative steps are unfolded into a deep interpretable iterative generative dual adversarial network (iGDANet). Generator in iGDANet is interwoven by multiple deep feature pyramid denoising modules and deep interpretable convolutional reconstruction modules. In each iteration, the generator establishes an adversarial game with the spatial and spectral discriminators to update both spectral and spatial information without ground-truth images. Extensive experiments show that, compared with the state-of-the-art methods, our proposed IU2PNet exhibits very competitive performance in terms of quantitative evaluation metrics and qualitative visual effects.