Magda, the short answer is no, you can't show two different work item types on the same custom list. The Kanban Board app is one of the exceptions- if this is an important requirement then you may want to consider that. If you run scrum teams or use Iterations then Team Planning and some of the other more important operational apps also treat stories and defects as siblings and show them together. Backlog management on the Plan > Backlog page works the same way.
The question that I'd put to your teams though would be this; what exactly is it that they want to do that they can't do using one of the existing pages or by placing more than one custom list app on a page? I have a large enterprise with ~1,500 users and this hasn't been a serious issue for us. We got a few complaints at first (we were used to Jira where everything is essentially the same object type) but when we challenged our teams to tell us exactly what they couldn't do and why it was important, no team had a valid use case (in this regard) that Agile Central couldn't handle.