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. (c) 2025 Optica Publishing Group. All rights, including for text and data mining (TDM), Artificial Intelligence (AI) training, and similar technologies, are reserved.