A multiple clutch module for an automatic transmission integrates at least two multi-plate wet clutches into a single module. Each of the clutches includes a set of separator plates interleaved with at least one friction plate and a piston configured to compress the separators plates and friction plates. The separator plates of the first clutch are splined to a housing along their inner diameter whereas the separator plates of the second clutch are splined to the housing along their outer diameter. Each piston is associated with an apply chamber and a balance chamber radially inside the respective separator plates and friction plates. The housing rotates about a central shaft. Pressurized fluid is supplied to the clutches from the shaft. The first and second balance chambers are connected by a passageway within the housing such that they can be supplied with fluid from a common orifice in the housing.