Diet and Iams have a history of using by-products and doing unethical animal research. I would definitely stay away from those.
I feed my dog Nature's Variety. She gets a little kibble in the morning, and the frozen raw food plus extra veggies and cottage cheese in the evening. They have a line called Instinct without grains in it. That is what the raw food is, but they also have canned and dry food, too. The food might be a little higher priced for 3 animals.
There is also Innova (also has a grain-free line called EVO), California Natural, Solid Gold, Merrick, Castor & Pollux, and Wellness. Wellness has a line for dogs where each one contains 1 protein and 1 carbohydrate (for dogs with allergies). I'm not sure about their cat food. Natures Logic is really good but higher priced. The dog I used to have liked it, but my current dog won't touch it. Not sure why, because it's very similar to the Natures Variety food she eats now.
One thing about the Natures Variety -- I noticed when I opened her last bag that it appeared to be a little darker in color. I have no idea why I didn't check with the company to see what the deal was. She has been itching and biting like crazy over the past couple months. I couldn't find fleas, had changed her dog cookies and then switched back, used a different shampoo. Then I just thought it might be allergies. Well, I opened a new bag of the dry food (had bought them at the same time). That's when I thought about the food being different. I was going to e-mail them and saw on their website that they opened a new plant and animals that were used to eating only one protein may experience temporary bowel issues. That says to me that they are making different types of food with the same equipment. I think that maybe Haley is allergic to something from another food being made there. I'm hoping the solution is that simple. However, it does make me mad that they have this issue with the new plant but not their other ones. Luckily I have part of a bag of the Instinct and started her back on that today (had quit giving Instinct because she had high BUN --kidney-- levels for a while and wanted to give her a food with a little less protein). I may have to find another brand. There are only a few that I'm extremely comfortable with and I already know she doesn't like the Natures Logic. I'll probably go with Innova if it turns out she is allergic to the new way Natures Variety manufactures their food. If you want to try Natures Variety (I'm sure not very many animals have her issues), they have a couple you can sign up to get that is a buy 1 bag (frozen or dry) and get 1 free.