I'm using MBAM (free version, not resident) with avast 5 (also free version) with no problems either. I know when avast 5 first came out there were compatibility problems with the paid version of MBAM, but I thought those had eventually gotten straightened out.
And I agree with the others about Ad-Aware, it's become little better than a disk-space hog (same's pretty much true of Spybot S&D). If you want a good "second opinion" companion for MBAM, many of us like SUPERAntiSpyware, often referred to as SAS.