The coupled cubic-quintic nonlinear schrodinger equations in fiber optics, which describe the effects of quintic nonlinearity on the ultrashort optical pulse propagation in non-Kerr media, are investigated. Using symbolic computation, we derive the dark-bright soliton solutions of such equations. By virtue of asymptotic analysis and graphical analysis, the overtaking and head-on elastic interactions of the two bright and dark solitons are presented. Mixed bound-state solitons also arise when all of the solitons propagate in parallel, displaying the beating effects due to the oscillatory terms, or displaying breather-like structures