In this study, we investigate the hierarchical microarchitecture formation of magnetic barium hexaferrite (BF) platelets in polydimethylsiloxane (PDMS) using electric and magnetic field assembly technique. First, external fields are applied to the colloidal solution to form the microstructure before curing the composites. After microstructure formation, the composites are thermally cured to freeze the microstructure. We investigate two different cases in this study-(1) magnetic field processed composites and (2) multi-field processed composites, which were processed under both magnetic and electric fields. We observe that macro-chains formed due to simultaneous application of electric and magnetic fields had a much higher length compared to the macro-chains formed due to just magnetic field. For both cases individual BHFs are found to be oriented in the direction of the external field. The analysis of SEM microstructures using ImageJ and MATLAB showed that at least two different levels of hierarchies are present in the microstructure for both cases, which are referred to as BHF stacks and micro-chains. From the experimental quantitative microstructure analysis, BHFs are found to be slightly better oriented (magnetic easy-axis direction in relation to the external field) at all scales for the electric and magnetic field processed composites compared to just the magnetic field processed composites. Magneto-electrohydrodynamics modeling of the polymer-particulate mixture predicts a similar behavior. Computational simulations are performed wherein particulates, subjected to both DEP forces resulting from an applied electric field, and magnetic dipole interactions in response to applied magnetic field, are allowed to form quasi-equilibrium structures before locking in a final structure to represent curing. Results from simulation confirms the finding on longer macro-chain formation similar to the experiment for the case of magnetic and electric fields compared to just magnetic field. Analysis of the microstructures from simulation also confirms that multiple levels of hierarchies are present in the composites' microstructure for both cases. In future, quantifying the corresponding metrics at each level of hierarchy will help to better understand the microstructure and can be served as input to the model and also used to validate the model.