Can relaxed and color treated hair coexist?

Yes it can but it all depends on how you maintain it. Is it recommended? No. Having double processed hair takes a lot of work to maintain. Work that very few know about or want to put in. If you have damaged hair don't go near the color, permanent ones at least. Rinses might be better for ladies who are nursing their hair back to health. Working on getting your hair healthy is top priority. I tried to have color treated and relaxed hair once before and it wasn't successful. My hair was constantly dry despite going to the shop every two weeks. She was telling me that my hair needed to be kept moisturized but wasn't telling me what to do about it. After that stint with highlights, I decided to leave it alone. Fast forward to 2013 and here I sit with relaxed and color treated hair. Some stylist will tell you to pick a chemical. If you want relaxed hair then don't get color and vice versa. Here a just a few tips to help you if you decide you want both. 

1. Make sure to keep protein in your hair. You can do hard protein treatments once a month or every other month. Or you can do like I do and use protein based products weekly to help keep some strength into your hair.
2. Moisture. Color dries the hair out and can cause unwanted breakage. Deep condition your hair often. When you do deep condition do it with heat i.e steam or a dryer to make sure the conditioner penetrates the hair shaft. Make sure that you are keeping up with moisturizing and sealing your hair. Do hot oil treatments. Anything that aides in keeping moisture in the hair is very beneficial.
3. Lay off the heat. Constant heat usage will do nothing to help the health of your hair. I'm not saying don't use it just use it very seldom.
4. When getting your hair colored don't go more than 2 shades lighter than your natural hair color. Doing so makes the hair more weaker. (From LaToyaJonesblog.com) 

Making sure you stick to these tips will help you to successfully have double processed hair. I am not a licensed stylist. I am just sharing the tips that have helped me to keep my relaxed and colored hair on my head and not on the floor. Thus not loosing any of the progress I have made on my hair journey.