We compare the performance, stability and microstructure of Si/Gd multilayers containing thin barrier layers of W, B(4)C, or SiN(x), and determine that multilayers containing 0.6 nm thick W barrier layers at each interface provide the best compromise between high peak reflectance in the extreme ultraviolet near lambda=60 nm and good stability upon heating. The Si/W/Gd films have sharper interfaces and also show vastly superior thermal stability relative to Si/Gd multilayers without barrier layers. We find that these structures have relatively small compressive film stresses, and show good temporal stability thus far. We measured a peak reflectance of 29.7% at lambda=62.5 nm, and a spectral bandpass of Deltalambda=9 nm (FWHM), for an optimized Si/W/Gd multilayer having a period d=32.0 nm.