A mode-locked solid-state laser containing a birefringent element is shown to emit synchronously two frequency combs associated to the two polarization eigenstates of the cavity. An analytical model predicts the polarization evolution of the pulse train, which is determined by the adjustable intracavity birefringence. Experiments realized with a Nd:YAG laser passively mode locked by a semiconductor saturable absorber mirror are in perfect agreement with the model. Locking between the two combs arises for particular values of their frequency difference, e.g., half the repetition rate, and the pulse train polarization sequence is then governed by the relative overall phase offset of the two combs.