Abstract: First-order phase transitions at the electroweak scale are predicted by many Standard Model extensions. They could create a stochastic gravitational wave background observable in the millihertz range today. The next-generation spaceborne observatory LISA has the potential of observing these backgrounds. However, possible phase transition signals will be buried under instrument noises and a foreground signal from millions of galactic binary systems. Here we explore the detectability of different phase transition models. We use statistical methods to recover a phase transition signal from data that is simulated using the LISA Simulation Suite, which allows for the injection of realistic instrument noises and a modulated binary foreground. We find that, by accounting for the modulation of the foreground, we are better able to constrain the phase transition parameters.