Dislocation transmission through α/β phase boundaries in titanium alloys is studied using integrated crystal plasticity (CP) and discrete dislocation plasticity (DDP) modelling techniques, combined with experimental micro-pillar compression test results. Direct dislocation transmission together with the nucleation of new dislocations ahead of a pile-up at an α/β interface, termed indirect slip transfer, are both assessed and their role in controlling microstructure-dependent strain rate sensitivity considered. A critical shear stress criterion for direct slip transfer across an α/β interface in Ti-6242 has been established by capturing the local slip penetration through the phase boundary using CP and DDP comparisons with experimental two phase micro-pillar compression. The competition between direct and indirect slip transfer has been investigated using a single Frank-Read source DDP model. Direct slip transfer is found to occur only under specific conditions which have been quantified. The strain rate sensitivity of dual phase titanium alloys is demonstrated to depend on average pile-up size which is significantly influenced by α/β morphology.