An aluminum brazing alloy composite sheet is provided which can be utilized in both the vacuum brazing process and the controlled atmosphere brazing process for the brazing of aluminum parts. The brazing alloy composite sheet consists of an aluminum core alloy of the 3XXX, 5XXX or 6XXX type clad at least on one major surface with a lithium-containing aluminum filler alloy containing from about 0.01% to about 0.30% by weight lithium. The core alloy may contain up to about 2% by weight magnesium and is suitable for producing aluminum alloy heat exchanger assemblies, such as radiators or evaporators.