We study the dynamics and stability of soliton optical frequency comb generation in a dissipative, coherently pumped cavity with both second- and third-order nonlinearity. Cavity sweep simulations and linear stability analysis based on path continuation reveal the existence of bistable solitons. These families of solitons represent a continuous transition between a purely quadratic and a Kerr cavity soliton frequency comb. Perspective demonstration of these novel, to the best of our knowledge, optical sources is an ongoing relevant subject within the frequency comb community.