In this paper, a neural network solution to extract independent components from nonlinearly mixed signals is proposed. Firstly, a structurally constrained mixing model is introduced to extend the recently proposed mono-nonlinearity mixing model, allowing that different nonlinear distortion are applied to each source signal. Based on this nonlinear mixing model, a novel demixing system characterized by polynomial neural network is then proposed for recovering the original sources. The parameter learning algorithm is derived mathematically based on the minimum mutual information principle. It is shown that unique extraction of independent components can be achieved by optimizing the mutual information cost function under both model structure and signal constraints. In this framework, the theory of series reversion is developed with the aim to perform dual optimization on the polynomials of the proposed demixing system. Finally, simulation results are presented to verify the efficacy of the proposed approach.