A coating system (14) for Si-containing materials, particularly Si-based composites used to produce articles (10) exposed to high temperatures. The coating system (14) is a compositionally-graded thermal/environmental barrier coating (T/EBC) system (14) that includes an intermediate layer (24) containing yttria-stabilized hafnia (YSHf) and mullite, alumina and/or an aluminosilicate, which is used in combination with an inner layer (22) between a Si-containing substrate (12) and the intermediate layer (24) and a thermal-insulating top coat (18) overlying the intermediate layer (24). The intermediate layer (24) provides environmental protection to the silicon-containing substrate (12), and has a coefficient of thermal expansion between that of the top coat (18) and that of the inner layer (22) so as to serve as a transition layer therebetween. The intermediate layer (24) is particular well suited for use in combination with an inner layer (22) of an alkaline earth metal aluminosilicate (such as BSAS) and a top coat (18) formed of YSZ or YSHf.