Some people complain that their antivirus software automatically stops working after 5 or 10 minutes when they were using both Avast and Malwarebytes at the same time.
The direct answer to the question is No! You can not use both pieces of software at the same time on a single system. READ: Does Lia Die In The Spirit Catches You and You Fall Down? Is it OK to run Avast and Malwarebytes at the same time?