Based on the biased one-photon photorefractive crystals, the solutions of incoherently coupled bright and dark soliton families governed simultaneously by linear and quadratic electro-optic effects were derived theoretically. The intensity profile and stability of soliton families were investigated. The different functions of the linear and quadratic electro-optic effects were discussed and the results show that, the interplay between the linear and quadratic electro-optic effects can enhance the photorefractive nonlinearity for bright soliton families but weaken the photorefractive nonlinearity for dark soliton families. Moreover, the bright soliton components can remain invariant during propagation process, and the dark soliton components show instability for long propagation distance.