The separation of incoherent emission signals from coherent light scattering often poses a challenge in (time-resolved) microscopy or excitation-emission spectroscopy. While in spectro-microscopy with narrowband excitation this is commonly overcome using spectral filtering, it is less straightforward when using broadband Fourier-transform techniques that are now becoming commonplace in, e.g., single molecule or ultrafast nonlinear spectroscopy. Here we show that such a separation is readily achieved using highly stable common-path interferometers for both excitation and detection. The approach is demonstrated for suppression of scattering from flavin adenine dinucleotide (FAD) and weakly emissive cryptochrome 4 (Cry4) protein samples. We expect that the approach will be beneficial, e.g., for fluorescence lifetime or Raman-based imaging and spectroscopy of various samples, including single quantum emitters.