We describe a fluctuating volume-current formulation of electromagnetic fluctuations that extends our recent work on heat exchange and Casimir interactions between arbitrarily shaped homogeneous bodies [A. W. Rodriguez, M. T. H. Reid, and S. G. Johnson, Phys. Rev. B 88, 054305 (2013)] to situations involving incandescence and luminescence problems, including thermal radiation, heat transfer, Casimir forces, spontaneous emission, fluorescence, and Raman scattering, in inhomogeneous media. Unlike