The universal bimodal distribution of transmission eigenvalues in lossless diffusive systems underpins such celebrated phenomena as universal conductance fluctuations, quantum shot noise in condensed matter physics, and enhanced transmission in optics and acoustics. Here, we show that in the presence of absorption, the density of the transmission eigenvalues depends on the confinement geometry of the scattering media. Furthermore, in an asymmetric waveguide, the densities of the reflection and absorption eigenvalues also depend on the side from which the waves are incident. With increasing absorption, the density of absorption eigenvalues transforms from a single-peak to a double-peak function. Our findings open an additional avenue for coherent control of wave transmission, reflection, and absorption in random media.