Can I get an adult cap to keep the soap out of my husband's eyes when washing his hair?

You can also use the rinse free shampoo caps, that have shampoo and conditioner all in one. You just warm it for a few seconds in the microwave, and then put it on his head and rub it around. It's very easy and mess and drip free. The ones I used were made by Comfort personal cleansing, and I ordered them at Walmart.com.
I had to use those right after I had my hip replacement surgery as I couldn't get in the shower for 7 days after my surgery.

Yes. There are lots on the market.

I usually ask a client to hold a clean, folded flannel over his eyes and to tilt his chin up (if he's able). Where are you washing your husband's hair, over the sink, in the shower, in the bath?

If it's getting very tricky, there are no-rinse shampoo caps which you pop in the microwave to warm, put over the person's head, massage gently, then remove and dispose of the whole cap. They work much better than you might think! - I was pleasantly surprised.

Those catalogs like Lillian Vernon used to have one that went around the head.

First, are you using one of the "no tears" baby shampoo products? If not try that.
A terry "sweatband" might help, it will absorb any excess that drips down.
I used wrist ones on myself when I was showering my Husband, it kept my arms drier and prevented my shirt sleeves from getting soaking wet.

Use a sun visor type hat, it goes around the head, has a bill that blocks water or soap, but is open at the top