My husband and I go to Disney 1-2 times a week (yes, a week!) as we live in Orlando and have annual passes
I'm well versed in healthy dining at Disney. And they've been working hard over the last few years to bring healthier options into the parks - there's tons of choices now!
Here's a link with all the menus at the parks:
http://allearsnet.com/menu/menus.htm
The table service restaurants will bend over backwards for your requests. Sometimes I find that the buffets are "easier" to eat at since I get my fill of salads and veggies, but it does take willpower to not gorge and to avoid the desserts. Also, the restaurants are very happy to split meals, which my husband and I often do. You can always just order appetizers as well.
For counter service, there are definitely healthy, interesting choices at each park. Take a look through the menus and make a plan of attack.
For Epcot, our favorite for healthy eating is Sunshine Seasons, and the Tangierine Cafe at Morocco is great as well.
At the Magic Kingdom, the Tomorrowland Terrance Noodle Station and Cosmic Rays both have lots of healthy choices, and Cosmic Ray's has a terrific condiment stand where you can load up on lettuce, tomato, mushrooms, sauteed onions, etc. Great for bulking up the grilled chicken sandwich or veggie burger.
At MGM/Hollywood Studios, we usually don't go for the counter service, but the Backlot Express has a great salad and veggie sandwich.
At Animal Kingdom, the fruit plate at Flame Tree BBQ is HUGE and very tasty, I just had it a couple weeks ago.
Oh, and lastly, since you are going at peak season, if there are any table service restaurants you want to visit, you need to make reservations! Ideally they should be made 180 days in advance (a lot of people do) but if you haven't yet, definitely get on that ASAP or you won't have any table service restaurants to choose from.
Good luck! Feel free to PM me if you have any specific questions.