Well, both Phil and I were down for the count today. We've both been fighting some sort of ick for quite a while now, and by this morning it was bad enough that neither of us felt up to going into work. This was a little unusual for us; in the 3years that we've lived together, this is only the second time we've been home sick together, and we're still figuring out how that works, exactly.
First and foremost, a good rule of thumb seems to be that one of you should not be spending too much time and energy taking care of the other if you're both sick. We've both spent the day trying to make the other lie down while we make soup and tea and put in a movie and fluff the pillows and do the laundry, but the fact of the matter is, we should BOTH be taking it easy. This isn't to say that you shouldn't take care of each other, but trade off on tasks; one of you gets up to make tea, the other one can go hunt down more DayQuil. It can be difficult, and may make you feel guilty that you're not doing more, but if nobody rests, nobody gets better.
Also, remember that a sick day is not the same as a weekend or a vacation day. Don't worry about looking cute for each other, and don't feel obligated to spend the whole day in each other's company. It's perfectly possible that your spouse would rather be left alone to cough and vomit in privacy, or just wants to sleep all day. Don't take it personally, and don't push too hard.
However, it's also possible that a sick day together can have its upsides. If you're both feeling up to it, cuddle in bed or on the couch (or make a nest out of pillows and blankets on the living room floor) and watch bad movies or read. Take naps together. Play games together. Just sit and talk for hours at a time.
Just make sure you both make the most of your sick days . . . even though they can be made fun, they'll get old after three or four in a row!