Jill Martz has written two articles on this topic ... two methods. Her articles are available on the web:
http://members.aol.com/hblossomxs/reverx1.html
http://members.aol.com/hblossomxs/reverx2.html

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From: Cappykw@aol.com
Date: Wed, 30 Jul 1997

A couple of days a question was asked in reguards to this and I see no one has answered . So, here goes:

[1] Thread up with ONLY 1 ply of floss--Come up as you always do and go down as usual

[2] DIFF PART-do this as many times as the number of floss you should be using (pattern calls for 3 ply so do this 3 times)

[3] Now do the other leg of the 'x (YES you are crossing as you go!)-Now on to the next 'x' and as you do so you will be making a single vertical(l) stitch to get to the next stitch.(Since this is done with a single ply of floss it is almost invisible.)

Hope this helps-but if it only serves to confuse PLEASE feel free to email me and I'll try to clear it up!

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From: Teresa
Date: Sat, 1 Nov 1997

I believe if you do you stitches this way, it will be reversible:

1st row:
/  /  /  /  /  /  /

skipping every other stitch and then cross them on the return:

X  X  X  X  X  X  X

and then fill in the holes:

X / X / X / X / X / X  

still going every other stitch as above and then cross on the return

XXXXXXXXXXXXXX

Read that somewhere, but have never tried it to see if it works.

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From: Kirsten Stevens kstevens7@juno.com
Date: Mon, 3 Nov 1997

The method I used was one I saw here on the list.

Use a single strand of floss. Complete each X as you go, repeating the stitch for as many strands thick as you desire.

So for a 2 strand effect you would do

      14,16   10,12      6,8   2,4
               X                        X
       9,11   13,15       1,3   5,7

for 2 X's side by side (up on odds, down on evens). The key here is that since you are using a single strand, the single vertical stitch you have to take between 4 & 5 and 12 & 13 is almost invisible. You also have to be VERY careful with hiding your tails and carrying over to other color blocks.

I suppose I could have backstitched it using the 1-2 8-7 3-4 6-5 method (can't remember the name), but I didn't know how I could successfully hide the tails!

(The next paragraph refers to using the method Teresa describes above): The problem with this method is moving on to the next row. Also, you would have vertical stitches on the last two X's of the row, and a double diagonal on the first stitch of the row. This method might work in a crunch or for a generally reversible effect, but it would have noticeable variations at the edges of rows.

Before you start ANY big project with reversible stitches, do something small! An ornament, bookmark, handkerchief... I did a very small bookmark, started in mid-September, finished only because I had to at the end of October. After about 50 stitches, I couldn't make myself want to work on it! I can't imagine doing something with multiple colors or a non-symmetrical pattern. Also remember, the reversable effect won't work if you plan on using letters or numbers in the pattern.

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From: "Kirsten Stevens"
Date: Wed, 28 Oct 1998

I stitched a small bookmark with reversible stitches on perf. paper. I will NEVER use that method again! It was tedious and IMHO not worth the extra effort.

The way I did it, you start with one strand of floss. Each X is worked one at a time. To start, repeat the bottom / as many times and the number of strands you would normally use for coverage. On perf paper, I wanted a 4 strand effect, so the / would be repeated 4 times, leaving a / on both the front & back. When you start your top \, you will have a vertical stitch on the back of your fabric, but it will only be one strand and therefore almost invisible. Repeat the top \ the same number of times.

I'll try some ascii art and hope proportional fonts don't mess it up too much! This would be 4 strand coverage.

                2,4
                6,8
        10,12  26,28  18,20
        14.16  30,32  22,24
              \ /\ /
               X  X
              / \/ \
          1,3  9,11   25,27
          5,7  13,15  29,31
               17,19 
               21,23

This method literally quadrupled the number of stitches I had to make. On top of that, you have to be very careful about burying your ends and making sure your vertical threads on the back are as unnoticeable as possible. My design was 3 Greek letters, placed vertically, and fortunately reversible themselves (like A,I and Y would look the same in a mirror). All the same color too.

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From: Cappykw@aol.com
Date: Tue, 4 Nov 1997

When I took the class we were taught----

[1] Use a single strand of floss (Even if pattern calls for 3 strands)

[2] Stitch the lst leg 3x(thus having done the 3 strands called for)

[3] Stitch the 2nd leg 3x

[4] Now go to next x

[5] When moving have only l strand to hide--almost invisible

If this is as clear as mud please email me and we'll try again!

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The Silver Needle has a reversible cross-stitch pattern for sale.
http://hometown.aol.com/silverthim/designs/reversible.htm