A number of multiphoton interference schemes involving independent fields from parametric down-conversion are analyzed. They include fourth-order (two-photon) interference between two fields from two independent parametric down-conversion processes, interference with two independent single photon Fock states (produced by gated parametric down-conversion), and quantum state teleportation and entanglement swapping. It is shown that the visibility in these interference experiments is related to a quantity that is responsible for the photon bunching effect in one of the fields (signal or idler) from the parametric down-conversion process. Besides the two-photon interference schemes, a four-photon interference scheme is discussed where we consider four-photon partition at a beamsplitter. It is found that probability distribution of the partition is dramatically changed by four-photon interference of six paths and the four-photon effect also depends on the same quantity responsible for photon bunching. We will discuss the difference between two-photon interference and four-photon interference.