Did you try opening the PSD directly from Illustrator? Also if there is an import function check to see what options are available. Sometimes it's different than using the "open" command and vice-versa. I've sometimes gotten stuff to work (or work better) because of that method.
You might be out of luck because your Illustrator is an older version. The only popular multi layered raster formats I know off the top of my head are PSD, PDF and also the newer layered TIFF option.
In the newer software I just tested out a PSD and it works. It also kept the type editable... when I created a PDF it kept the layers, but it converted the type to paths. You wont be able to edit it, but it will print better than printing your type from a photoshop file.
Seriously you may just be better off highlighting and copying the text from your layers then pasting into Illustrator (if you don't have any effects applied). I can't imagine you have that much text for a cab project, but then again I have seen some crazy stuff around here...
As some general advice the best way to send your work to the printer is send the Illustrator file (or whatever vector/ layout software was used) and link to your raster graphics (included in a separate folder). Don't in-bed the images... it only makes things more of a pain in case the production person needs to tweak your file for printing properly. Like for a common example, in case you forgot to convert a picture to CMYK...
Always check with the printer what options they prefer, for example now some printers use an RGB process to print on backlight films (perfect for marquees!). Most good printers provide a format guide for you to follow before submitting work and ask questions if you are unsure. You might save yourself some headache further down the road.
A lot of my experience comes from a traditional style screen and offset printer (film, to plate). These newer, low volume digital printers have different capabilities and requirements. So again, that is why I emphasize talking to the printer you are going to work with. Even if it's as simple as the neighborhood Kinko's...
Good luck!
-baker