The solitary wave coupled equations were solved numerically to study the characteristics of bright-dark soliton family. The steady-state solution and stability of soliton family supported by the combined action of the linear and quadratic electro-optic effects were analyzed. The results show that the total intensities of bright soliton components are slightly larger than that of dark soliton components in the bright-dark soliton family when the external bias field is positive and in this case, the nonlinearities result from the linear and quadratic electro-optic effects reinforce each other. When the external bias field is negative, the total intensities of bright soliton components are slightly smaller than that of dark soliton components in the bright-dark soliton family and the nonlinearities result from the linear and quadratic electro-optic effects either cancel out. Moreover, every component in bright-dark soliton family propagates stably.