We develop a general theory of birefringence and dichroism to account for the optical (and electrical) anisotropy exhibited by the refractive indices and attenuation coefficients of biological tissues or of composites of aligned particles. The primary bases for dichroism are the same as we considered before for birefringence (i.e., anisotropic parameters of the particles and of the embedding medium, and anisotropic shapes of the particle and configurational-correlation surfaces), but now the particle parameters are complex to include energy losses. The present birefringent effects are therefore more varied than those considered earlier, and the associated dichroic effects also depend on the refractive and absorbtive properties of the particles. Because the attenuation includes both absorption and scattering losses, scattering dichroism determined by particle shape and configurational fluctuations may be physically significant even if the particles are nonabsorbing and their refractivity is isotropic. The general theory, applied to phenomena involving both dichroism and birefringence, may account for some reported anomalies. We show, for example, that the presence of absorption in birefrigence measurements in which the base index is varied could be misinterpreted as intrinsic birefringence.