I use a dark charcoal black for my base color, not black. For example, I like Tamiya's acrylic NATO Black for that base. Then my shadow color will have a little black in it, and my highlights, a little dark grey. I've used other colors to modulate the shades and highlights, too-Prussian blue, for example.
For the satin color, though, you might even use a trick I remember from the Andrea "Painting Women" book. It was the section on using an airbrush, and the figure had long black evening gloves on (and not much else). The painter mixed some silver into his process, to help replicate the sheen that the fabric has. I don't remember the exact process-maybe someone else remembers and can describe it better or show examples. I have the book at home and can reference it when I get home tonight.