There are lots of people who keep them together, but that doesn't mean it is the best way. It works for some people, and ends up as a very expensive mistake for many others. It is more likely to work out for you and your fish if you go with one or the other, it is just too likely to cause problems. You have enough to worry about with these fish without increasing the risks of starvation and disease.
Compatibility is a tricky subject. What works for some can go against every 'rule' of fishkeeping. I have kept a lot of things together at one point or another and luckily (for them) it worked out. That does not mean I go and tell everyone to keep oscars with barbs and tetras or bichirs with discus. This is one that is closer to that invisible line of yes or no than most other cases of compatibility, but from my experience it is on the no side of the line. You will enjoy the fish more if you pick one or the other. You can sit down and see angels doing great, not angels doing great, a couple discus look like they are eating, and 'oh no, what's wrong with my....'