I've been doing some research to find healthy foods that kids will eat. From my own experience as well as some interesting articles on health foods that children will allegedly consume.
This article for example:
http://www.cookinglight.com/eating-smart/nutrition-101/healthy-foods-kids-00412000068618/
#1) Flaxseed- Very very healthy for the kiddos- However, you have to sneak this one in. They suggest sprinkling it on cereal or cutting it into pancakes. I have my doubts that this would fly with the boys. I am however, tempted to try it. Do you think your kids would be willing?
#2) Tofu- I haven't tried a Tofu smoothy- I harbor doubts.
#3) Sweet Potatoes!!1 YES! Finally one I can point to and say "YES! My kids love SWEET Potatoes!!" We make Sweet potato fries with a bit of Greek seasoning- they LOVE it!
This article also included yogurt (they love it), hummus (they don't), salmon burgers (ew), avocado (well, I like it), and finally mangoes (big yes). Do your kids enjoy any of these foods?
The: "Decidedly no" face.
There are different approaches to encouraging children to eat healthy. One idea is to make the food very pleasing to the eye. If you have the talent like this mom I applaud you!
http://www.mymodernmet.com/profiles/blogs/samantha-lee-pop-culture-food-art-instagam
Below image is found in the above link
Check out some of these ideas:
http://www.parenting.com/gallery/fun-recipes-for-kids?pnid=112461
below image from above link
Here's the bottom line though, it takes experimentation. Through experiments with new foods, unique or attractive presentation, or fun ways to eat the food- it can help children as well as parents, start making positive changes to their diet!