The distributed hybrid flow shop scheduling problem (DHFSP), which integrates distributed manufacturing models with parallel machines, has gained significant attention. However, in actual scheduling, some adjacent machines do not have buffers between them, resulting in blocking. This paper focuses on addressing the DHFSP with blocking constraints (DBHFSP) based on the actual production conditions. To solve DBHFSP, we construct a mixed integer linear programming (MILP) model for DBHFSP and validate its correctness using the Gurobi solver. Then, an advanced iterated greedy (AIG) algorithm is designed to minimize the makespan, in which we modify the Nawaz, Enscore, and Ham (NEH) heuristic to solve blocking constraints. To balance the global and local search capabilities of AIG, two effective inter-factory neighborhood search strategies and a swap-based local search strategy are designed. Additionally, each factory is mutually independent, and the movement within one factory does not affect the others. In view of this, we specifically designed a memory-based decoding method for insertion operations to reduce the computation time of the objective. Finally, two shaking strategies are incorporated into the algorithm to mitigate premature convergence. Five advanced algorithms are used to conduct comparative experiments with AIG on 80 test instances, and experimental results illustrate that the makespan and the relative percentage increase (RPI) obtained by AIG are 1.0% and 86.1%, respectively, better than the comparative algorithms.