I also sometimes sleep with my eyes partly open, according to my husband (who is indeed somewhat creeped out by it). Like you, I have dry eye, as well, which in my case is caused by poor functioning of the little Meibomian oil glands at the base of the eyelashes (rather than by lack of tears, which is another cause).
Here's what works pretty well for me:
At least once a day, without fail, warm eye packs for about four minutes. You can buy these cloth-covered, rice-filled things at places like Bed Bath and Beyond, and they're worth their weight in gold for those like me with the oil gland problem. I just put my eye pack in the microwave for a few seconds, only enough to warm it a bit--not ever, ever hot.
During the day, Systane Eyedrops every few hours. If my eye is dry when I wake up, putting some of these drops in right away is a big help.
Before bed, a thick eye ointment. You can buy various types over the counter, paying quite a bit of money for a wee tube. They're usually a mixture of mineral oil and petrolatum. Some of them, like LacriLube, are very, very thick, being mostly petrolatum with a tiny bit of mineral oil. Those I find irritating.
My eyes get along better with a somewhat cheaper, generic version that's about 42% mineral oil and 57% petrolatum.
Finally, I recommend a great site for those with dry eyes. Not surprisingly, it's call Dry Eye Zone. Lots of people there share their ideas on how to deal with this condition:
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