An umbrella valve includes an umbrella-valve body having a stem, a flexible umbrella, and a flange. The umbrella and the flange are each attached to, and extend radially outward from, the stem. The flange has at least one fluid passage. The umbrella valve can be placed in a valve housing having a sealing-surface portion. The umbrella, when the umbrella-valve body is placed in the valve housing, is pushed away from the sealing-surface portion under a forward fluid flow and is pushed against the sealing-surface portion under a reverse fluid flow. An umbrella-valve assembly includes the umbrella valve and the valve housing.