In this work, we use the transfer matrix method to optimize TPBi capping layers deposited on organic light emitting diodes with respect to light extraction and transmittance. The green transparent organic light emitting diodes comprise three organic semiconductors (CBP, Ir(ppy)₃ and TPBi) forming an efficient simplified phosphorescent organic light emitting diode stack. A transparent cathode of 2 nm Cs₂CO₃, 2 nm Al and 16 nm Au is deposited by thermal evaporation. The diode stack as well as the capping layer are deposited by organic vapor phase deposition. The refractive indices and extinction coefficients of all materials in the transparent organic light emitting diodes (glass, indium tin oxide, organic semiconductors and cathode) are determined using spectroscopic ellipsometry combined with optical transmittance and reflectance measurements. With these spectrally resolved data, we calculate the transmittance of transparent organic light emitting diodes with TPBi capping layers of different thicknesses. The results were validated with high accuracy in the visible spectral range and beyond (360 nm-1000 nm) by a series of experiments. By choosing a TPBi capping layer of optimized thickness (here 50 nm), we fabricated transparent organic light emitting diodes with an optical transmittance which was strongly enhanced from 47% (reference without capping layer) to 65%, measured at 555 nm.