  Using a three-dimensional (3d) effective field theory and non-perturbative
lattice simulations, we study the MSSM electroweak phase transition with two
dynamical Higgs doublets. We first carry out a general analysis of spontaneous
CP violation in 3d two Higgs doublet models, finding that this part of the
parameter space is well separated from that corresponding to the physical MSSM.
We then choose physical parameter values with explicit CP violation and a light
right-handed stop, and determine the strength of the phase transition. We find
a transition somewhat stronger than in 2-loop perturbation theory, leading to
the conclusion that from the point of view of the non-equilibrium constraint,
MSSM electroweak baryogenesis can be allowed even for a Higgs mass mH \approx
115 GeV. We also find that small values of the mass parameter mA (\lsim 120
GeV), which would relax the experimental constraint on mH, do not weaken the
transition noticeably for a light enough stop. Finally we determine the
properties of the phase boundary.
