First of all, don't ever give up! Some kids are just naturally picky, but over time, if you keep offering healthy foods, they will learn to like them. The key here is that you and your partner are good examples of loving to eat the veggies and fruits, and continually teaching them WHY they need these foods. Make sure they have no allergies going on. Some kids find orange juice or other foods irritate their stomachs. Other kids, who may have hay fever or other non-food allergies going on just want to eat what will go down easily because the allergy symptoms have their taste buds off, and their sinuses full of mucous, which can make swallowing more difficult. If they have any tooth problems, chewing more fibrous foods (fruits and veggies) can be challenging. Finally, just know that some kids want to take the easy way out, more flavor, less chewing, slides down easy, satisfies the hunger monster. You may have simple carb addicts on your hands. Keep insisting they eat at least one bite of everything you put on their plates. Find a good multivitamin they like to cover what they are missing. One thing I did for my kids when they were small was put things they woudln't eat into things they would eat, like adding pureed beats to chocolate cake or making 'green eggs and ham' just like the Dr. Seuss book (which was spinach pureed into the scrambled eggs)!
One more point I thought of: try different forms of the fruit or veggie you are trying to get them to eat. If they don't like applesauce, let them eat the fresh apple, it is better! If you are trying fresh veggies, try steaming or lightly cooking them. It does change the flavor/texture. If you are trying canned veggies, try fozen, or vice versa. My kids hate all canned veggies, and I don't like serving them anyway becasue of the lower nutritional value and loss of texture, color, and flavor... but if your will accept canned veggies, it may be a a good starting point.
I hartily agree with the suggestion that picky eaters should eat the veggie before the entre is served! Now that my kids are older (teenagers), make room for their likes/dislikes. But all three of them eat nearly everything I fix, and they are all quiet healthy, so it's worth the effort!
Good luck, and again, never give up!