We use a fiber-based double-slit Young interferometer for studying the far-field spatial distribution of the
two-photon coincidence rate (coincidence pattern) for various quantum states with different degree of spatial
entanglement. The realized experimental approach allows us to characterize coincidence patterns for different states without any modifications of the setup. Measurements were carried out with path-entangled and separable states. The dependence of the coincidence pattern on the phase of the interferometer for superposition and separable states was studied. The results have implications for using of nonclassical light in multiphoton imaging, quantum lithography, and studies of phase decoherence.