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You can find photos of buttonholes in  Encyclopedia of Tunisian Crochet!
Buttonhole Stitch  

Use Tunisian Knit or Simple sts for background.
Row 1- Forward: *pull loops on hook for the background st, skip 3+ sts (depending on the desired size) to form Buttonhole. *Repeat to end of row, alternating loops and Skipped stitches for desired pattern.
Row 1-Return: Return as you normally would up to skipped stitches. Crochet equal number of chains as skipped stitches (if you skipped 3 stitches, then work 3 chains). *Repeat to end of row.
Row 2 Forward: Pull loops up as you normally would for Tunisian Crochet.  When you come to a Buttonhole, insert the hook into each chain used to create the buttonhole, yo, and pull a loop onto hk.
Row 2 Return: Return as you normally would for Tunisian Crochet.
Design patterns with buttonholes.
Repeat Rows 2 and Eyelets for rest of piece, alternating Eyelets with background st to create desired pattern.  
Tip:  Alternating Patterns can include checkerboard or diagonal stripes.  Forming Horizontal stripes with Eyelets is not a practical application of this st; it can be done, but will create a weak spot in the finished product. Vertical stripes can be done, but will have the chs visible in each row.

Checkerboard Pattern with Buttonholes

When crocheting ch for beginning, be certain to use a number that is divisible by the size of your eyelet. If your eyelet is 5 spaces long, then you should chain 25 or 50 or 65 or 105 etc to fit your desired width. If your Buttonhole is 3 spaces long, ch 48, 72, 99, or 108, etc. to fit your desired width.
Always add 2 extra stitches to form the edges of your piece.
Rows 1 & 2 Forward and Return: follow instructions of Afghan or
Tunisian Stocking stitches.
Row 3 Forward: pull equal number of loops on hook as desired length of Buttonhole (if Buttonhole is 5 spaces, pull 5 loops on hook). Alternate between loops and Buttonholes.
Row 3 Return: follow instructions for forming Buttonholes.
Row 4 Forward and Return: Repeat Row 2.
Row 5 Forward: pull loops on hook twice the number of spaces for Buttonhole. (Buttonhole is 5 spaces, pull 10 loops on hook), *skip number of spaces for Buttonhole, pull loops on hook same number as Buttonhole. *Repeat to end, making certain the last 2 groups of stitches are all loops to add stability to the finished piece.
Row 5 Return: follow instructions for forming Buttonholes.
Row 6 Forward and Return: Repeat row 2 or 4.
Alternate Even and Odd numbered rows to create the checkerboard
pattern.

Diagonal Stripes with Buttonholes
When crocheting ch for beginning, be certain to use a number that is divisible by the size of your Buttonhole. If your Buttonhole is 5 spaces long, then you should chain 25 or 50 or 65 or 105 etc. to fit your desired width. If your Buttonhole is 3 spaces long, ch 48, 72, 99, or 108, etc. to fit your desired width.
Always add 2 extra stitches to for the edges of your piece.
Rows 1 & 2 Forward and Return: follow instructions of Afghan or Knit stitch.
Row 3 Forward: *Pull loops on hook twice the number desired for Buttonhole size. (If eyelet is 5 sts long, then pull 10 loops on hook), skip # of sts for Buttonhole. *Repeat to end of row, making certain to end with loops to add stability to finished product.
Row 3 Return: Follow instructions for forming Buttonholes.
Row 4 Forward: Pull loops on hook, but move over (left or right-your choice)the number of sts equal to number of sts in Buttonhole. Alternate Buttonholes with twice the number of loops to end of row. (5 Sk sts for Buttonhole, 10 loops between the Buttonholes.)
Row 4 Return: follow instructions for forming Buttonholes.
Repeat Row 4 to finish piece, making certain to add Buttonhole groups on one end to maintain pattern. (On about Row 6, you will need to add another Buttonhole group on one end to start a new diagonal stripe. Then add more Buttonhole groups as needed to maintain pattern).
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For a diagram of all the various Threads of a Tunisian Crochet Stitch,
Click Here!
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Abbreviations:  
Beg: Beginning
 Ch: Chain stitch   
Lp: Loop  
Hk: Hook
DO: drop off
PU: pick up
Sk: skip stitches
Sl St: slip stitch
Yo: Yarn Over hook
Tks-Knit st  
Tss-Simple/Afghan St Tps-Purl St
 Trs-Reverse St
 Tfs-Full/Plain St

Trps-Reverse Purl st