In this paper we present the stabilization of the pulse repetition rate of dual-comb lasers using an intracavity semiconductor saturable absorber mirror (SESAM) for passive modelocking and an intracavity birefringent crystal for polarization-duplexing to obtain simultaneous emission of two modelocked beams from the same linear cavity sharing all components. Initially surprising was the observation that the cavity length adjustments to stabilize one polarization did not significantly affect the pulse repetition rate of the other. We gained insight in the underlying physics using both a semiconductor and Nd:YAG laser gain material with the conclusion that the pulse arrival timing jitter of the two beams is decoupled by the uncorrelated time delay from the saturated SESAM and becomes locked with sufficient but not too much pulse overlap. Noise stabilization is in all cases still possible for both combs. The dual-comb modelocked laser is particularly interesting for the semiconductor laser enabling the integration of gain and absorber layers within one wafer (referred to as the modelocked integrated external-cavity surface emitting laser--MIXSEL).