Plumbing Question? Leaves coming through the pipes into my bathtub?

Every time after a big rain we turn our water faucet on to wash hands,brush teeth,bathe ect... and little pieces of leaves come out of the faucet with the water. I dont what could cause leaves to come through the pipes and into a bath? our gutters are clogged beceuse of all the rain. and there is a big tree outide that extends over the house.