Let's get the terminology straight first. The "tread" is the part of the stair you step on. At the back of every tread, you will usually have a "riser", although open stairs don't have risers. And on neither, one or both sides of the stair, you can also have a "stringer". Stringers have notches cut out of their bottom edge to accomodate the treads and risers.
When you say "face" of the stairs, do you mean the riser or the front vertical surface of the tread. Also, can you explain what is causing these "faces" to look terrible? Are they damaged in some way, are they coated with adhesive?
Finally, Johnsonite makes a large variety of solid vinyl residential stair nosings. Go to this page:
Johnsonite > Finishes & Accessories > Stairwell Management
And click on the link "Download the Stairwell Management Brochure PDF". That brochure is only 8 pages long, but it starts on page 84 and ends on page 91 (since it's part of a larger catalogue).
On the last page of that brochure you will find a variety of solid vinyl stair nosings that are molded in such a way as to allow you to use material up to 3/8 inch thick under the nosing on the riser. If you can't clean up your risers, you could use these vinyl nosings and install 3/8 inch thick plastic laminate flooring material on your risers. You could use carpeting on the threads themselves, and the vinyl nosings would make this a DIY project.