Also I wanted to add my experience. I spoke to my first in English (my native language) for his first year and then decided we should both speak to him in Spanish (my 2nd language-fluent). It was hard to switch, but once I had made the decision and stuck to it, it became easier and easier.
Now I have decided to switch back to English, and again it was very uncomfortable at first--not only making the switch, and remembering to do it, but taking into account my feelings about them having Spanish as their native language and feeling like they might be losing something.
Anyway, I just thought this perspective might help some of the other parents. They should know, yes it is very hard when you start, the children won't understand you, you'll feel uncomfortable, but it gets easier every day. I also taught immersion Spanish Kindergarten to English-only students so I know what it feels like to have kids looking at you with a blank face. It will be easier to make the switch than you might think. It helps if you think of it as the way you speak to a baby--of course, they don't understand you word for word but they learn through context, repetition, nonverbal clues, etc.
As for the other parent not understanding the language, it could become a special thing for the children and one parent. It might help to introduce a very structured daily ritual--not formal lessons, but just a *special* time with mom/dad where they use the other language in a very natural way. Bedtime stories could be only in the 2nd language, for example. Or, weekend mornings out to a restaurant where the language is spoken. The English-dominant parent can stay home and take a break and not feel left out
This kind of structure might help some parents who find it hard to make the switch--they could find it easier to organize their brains into using the language in a limited situation with certain activities, where the vocabulary would come more easily.