The paper focuses on the identification of discrete-time bilinear forms in the special case when the external noise (disturbance) is an autoregressive average moving process. The proposed estimation procedure is iterative where, at each iteration, two sets of parameter vectors are estimated interactively. Using the hierarchical technique, a hierarchical generalized extended least squares-based iterative (H-GELSI) algorithm is proposed for avoiding estimating the redundant parameters. In contrast to the hierarchical generalized extended gradient-based iterative (H-GEGI) algorithm, the proposed algorithm can give more accurate parameter estimates. The main results derived in this paper are verified by means of both the computational efficiency comparison and two numerical simulations.