The interaction of two coupled binary matter wave bright solitons is investigated by means of the variational approach in the presence of spatially varying nonlinearity. The effective potential characterizing the interaction between the two solitons is obtained. It is shown that the effective potential is composed of three parts, related to the spatially modulated nonlinearity, the external trapping potential and the interaction of the two coupled solitons. The spatially modulated nonlinearity induces a pseudo-potential and the solitons can be accelerated by the spatially modulated nonlinearity. The effect depends on the sign and value of the spatially modulated coefficient. The interaction of two coupled binary matter wave bright solitons is of short range, and may be attractive or repulsive depending on the sign of the interspecies interactions. Under the appropriate condition, the two coupled solitons can evolve stably and do not coalesce. The neighbouring binary Bose-Einstein condensates are also available as media to create symbiotic bright solitons. The validity of the theoretical predictions is verified by the numerical integration of the coupled Gross-Pitaevskii equations.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)