This paper describes an integrated setup for fluorescence recovery after photobleaching (FRAP) for determining translational and rotational Brownian diffusion simultaneously, ensuring that these two quantities are measured under exactly the same conditions and at the same time in dynamic experiments. The setup is based on translational-FRAP with a fringe pattern of light for both the bleaching and monitoring of fluorescently labeled particles, and rotational-FRAP, which uses the polarization of a short bleach light pulse to create a polarization anisotropy. The fringe pattern of the probe beam is modulated in conjunction with a synchronized lock-in amplifier giving a fast, sensitive, ensemble-averaged measurement compared to microscope-image based techniques. The experimental polarization geometry we used ensures that the fluorescence emission is collected without polarization bias. Therefore, only the orientation of the absorption dipole moment of the fixed dye in the particles is measured, which simplifies interpretation of the data. The polarization is modulated rapidly between two orthogonal polarization states, giving the polarization anisotropy in one, single measurement. The rotational and translational Brownian diffusion of anisotropic colloids is measured for ellipsoids of revolution. This experiment shows that in this case the rotational correlation function matches a three-exponential decay in accordance with theoretical predictions.