This work studies the model identification problem of a class of post-nonlinear mixture models in the presence of dependent latent components. Particularly, our interest lies in latent components that are nonnegative and sum-to-one. This problem is motivated by applications such as hyperspectral unmixing under nonlinear distortion effects. Many prior works tackled nonlinear mixture analysis using statistical independence among the latent components, which is not applicable in our case. A recent work by Yang et al. put forth a solution for this problem leveraging functional equations. However, the identifiability conditions derived there are somewhat restrictive. The associated implementation also has difficulties—the function approximator used in their work may not be able to represent general nonlinear distortions and the formulated constrained neural network optimization problem may be challenging to handle. In this work, we advance both the theoretical and practical aspects of the problem of interest. On the theory side, we offer a new identifiability condition that circumvents a series of stringent assumptions in Yang et al.’s work. On the algorithm side, we propose an easy-to-implement unconstrained neural network-based algorithm—without sacrificing function approximation capabilities. Numerical experiments are employed to support our design.