Hi Rem,
There are tons of good CMS systems out there and many of them are even free. DotNetNuke is probably the most robust that I have used and CMS made simple is a great, easy-to-use CMS that would be a good option for integration depending on your AwareIM back-end database of choice.
There are various levels of integration from shared sessions and databases on one end to simply utilizing iframes in one or the other applications on the other end. However, your lack of html and probably php knowledge is going to make integration a difficult if not almost impossible task for you.
What I would suggest is to stick with AwareIM and you can probably do the bulk of what you are trying to achieve. Site aesthetics are going to be a little restrictive but technically most cms type functionality should be possible. The addition of html formatted text fields with a wysiwyg editor is key to your ability to offer this type of solution.
Even with AwareIM, basic html knowledge is a real asset so you might want to study up a little bit. There are many sites out there that offer tutorials and such and you might find that an hour or two spent learning html might be time well invested.
Let me know if there are any specific cms challenges that you need help with.
Cheers,
Pete