To prevent Avast from scanning everything while MBAM scans, you should exclude MBAM in Avast Settings - Exclusions:
How to exclude Malwarebytes' Anti-Malware (MBAM) from Avast! 5.x:
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Sorry but that won't stop avast from scanning files that MBAM opens to scan, if those files are scanned in place, then depending on the file type avast will scan them (generally those that present an immediate risk, executables and those targeted by malware). By excluding MBAM files only excludes those files from being scanned, it doesn't ignore/exclude the processes/actions, e.g. the files it opens for scanning.
This mask covers all files in the folder so all of the files excluded in the Malwarebytes' Anti-Malware before this are a waste of time anyway.
C:\Program Files\Malwarebytes' Anti-Malware\*
Excluding a complete folder will obviously leave it less secure as nothing in it would be scanned.
I only have the free version and I have nothing for MBAM excluded on my XP or win7 systems.
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The major area to exclude in MBAM (Pro) for avast isn't actually in the avast folder but in c:\windows\temp\_avast5_ folder as that is where avast unpacks files it is going to scan.