Believe it or not, you have options when it comes to eating healthy. Sure, your tastes will adjust and change as you move your meals to healthy options but if you're like me, there are some foods that you just aren't going to like no matter how they are prepared. My list includes peas, sauerkraut and papaya among a few others. The good news is that, regardless of the health benefits you're looking for, there is almost always another option or an alternative preparation that you might like better. I strongly believe that life is too short to eat food you don't enjoy, even (especially!) if you're eating healthy.
For example, my husband doesn't like raw carrots but he eats these caramelized cumin roasted carrots like they're candy. They take about 2 minutes to prep when you buy a bag of baby carrots and use ground cumin, which we always have around. I strongly suggest getting the big bag of baby carrots because these will disappear before you know it. We seriously grab one out of the pan every time we walk by it. My two year old loves these also.
Another example. I think quinoa is disgusting. I know it's trendy right now and it has all sorts of health benefits but I just can't stand the taste or the texture. Neither can my hubby. The thing is, though, part of the benefit of quinoa is to reduce the consumption of nutritionally stripped white rice and pasta by replacing it in recipes. So, instead of white rice and pasta, sometimes we do whole wheat cous cous, which we love, or brown jasmine rice, which we don't totally love so I usually mix with the white jasmine rice. The way I see it, a little good is better than none and every little bit counts. You would try whole wheat or spinach pasta as other alternatives. Try different things until you find one you like!
I'd love to hear what other healthy foods your family has come to love or which ones you're currently eating for the health benefits but not totally loving. I always find it really interesting to hear what are a person/family's go-to meals or snacks.