The stability of two semiconductor lasers that are spatially separated by a passive resonator is analyzed using the composite-cavity mode approach. We study the nonlinear interactions of three composite-cavity modes and identify regions of in-phase and out-of-phase laser locking in the parameter plane of the transmission coefficients of the coupling mirrors and the laser length difference. Bifurcation analysis shows that the structure of the locking regions strongly depends on (i) the length of the passive resonator and (ii) the amount of amplitude-phase coupling of the laser field. Specifically, we find a single locking region when the passive resonator and the lasers have comparable lengths and up to three separate locking regions when the passive resonator is much shorter than the lasers. Furthermore, we use the recently developed 0–1 test for chaos to uncover intricate regions of chaotic dynamics that shrink in size and eventually disappear as the passive resonator length becomes comparable to the laser length.