We report a molecular dynamics simulation investigation of self-assembly and complex formation of charged neutral double hydrophilic and hydrophobic-hydrophilic block copolymers (BCP) with oppositely charged surfactants. The structure of the surfactant micelles and the BCP aggregation on the micelle surface is systematically studied for five different BCP volume fractions that also mimics a reduction of the surfactant concentration. The local electrostatic interactions between the oppositely charged species encourage the formation of core shell structures between the surfactant micelles where the surfactants form the cores and the charged blocks of the BCP form the corona. The emergent morphologies of these aggregates are contingent upon the nature of the BCP neutral blocks. The hydrophilic neutral blocks agglomerate with the micelles as hairy colloidal structures while the hydrophobic neutrals agglomerate in lamellar structures with the surfactant micelles. The distribution of counterion charges along the simulation box shows a close-to-normal density distribution for the hydrophilic neutral blocks and a binodal distribution for hydrophobic neutral blocks. No specific surfactant concentration dependent scaling relation is observed as opposed to the simpler case of homo-polyelectrolytes.