Microlenses with typical stellar masses (a few M⊙) have traditionally been disregarded as potential sources of gravitational lensing effects at LIGO/Virgo frequencies, since the time delays are often much smaller than the inverse of the frequencies probed by LIGO/Virgo, resulting in negligible interference effects at LIGO/Virgo frequencies. While this is true for isolated microlenses in this mass regime, we show how, under certain circumstances and for realistic scenarios, a population of microlenses (for instance stars and remnants from a galaxy halo or from the intracluster medium) embedded in a macromodel potential (galaxy or cluster) can conspire together to produce time delays of order one millisecond, which would produce significant interference distortions in the observed strains. At sufficiently large magnification factors (of several hundred), microlensing effects should be common in gravitationally lensed gravitational waves. We explored the regime where the predicted signal falls in the frequency range probed by LIGO/Virgo. We find that stellar mass microlenses, permeating the lens plane, and near critical curves, can introduce interference distortions in strongly lensed gravitational waves. Lensed events with negative parity, or saddle points (which have never before been studied in the context of gravitational waves), and that take place near caustics of macromodels, are more likely to produce measurable interference effects at LIGO/Virgo frequencies. This is the first study that explores the effect of a realistic population of microlenses, including a macromodel, on strongly lensed gravitational waves.