Phase-sensitive femtosecond-pulse interferometry was used to study both diffusive and coherent propagation of light in strongly scattering porous GaP. This material is a doubly-connected random network made by electrochemical etching. As the refractive index of GaP is large (3.3) and the bandgap is in the visible (550 nm), we expect strong scattering and negligible absorption in the red part of the visible spectrum. These samples have been well characterized by measurements of the total transmission and enhanced backscattering. Here, ultrashort-pulse interferometry is used to study the dynamic properties of the scattered light. This technique allows us to separate diffuse light from light that has propagated coherently through the sample. This makes it possible to obtain both the energy transport velocity and the group velocity. For the most strongly scattering samples we find deviations from normal diffusive behavior. Because the scattered pulses are measured interferometrically the phase of the scattered light in single speckles can also be obtained. This way, we are able to measure the distribution of fluctuations in the phase as well as in the amplitude and the pulse arrival time. These results are compared to existing theory.