Thanks for the suggestion pbust, as I mentioned earlier I had fixed this by adding exceptions for both the folder and the process in Bitdefender. For a few days I had no issues, but then yesterday I installed the new Windows 10 updates:
http://www.ghacks.net/2015/08/27/microsoft-releases-windows-10-patches-kb3081452-kb3081448-and-kb3081449/
And rebooted into the same 0135 error when opening cmd/iexplore. Interestingly enough the trick that jord mentioned works, but he's wrong about something, SysWow64 is the 32-bit folder (I know, confusing right? But hey that's Microsoft) so I think you're definitely right that there's some kind of hooking conflict going on with the 64-bit part of Windows, MABE and Bitdefender. I then followed your uninstall/reinstall steps and it works fine again, it's really weird but I guess I'll just be wary of Windows updates from now on, seems like they reset something? In your tests, do you have UAC activated? That might be something to look into as well, I personally have UAC on.
Also, I noticed something interesting in the mbae-service.log:
"2015-08-28T16:14:46.612-05:00";"SYSTEM";"1";"1.07.1.1015";"";""
"2015-08-28T16:46:05.798-05:00";"SYSTEM";"1";"1.07.1.1015";"";""
"2015-08-29T11:49:34.192-05:00";"SYSTEM";"1";"1.07.1.1015";"";""
"2015-08-30T10:39:11.130-05:00";"SYSTEM";"1";"1.07.1.1015";"";""
"2015-08-30T13:34:48.267-05:00";"SYSTEM";"1";"1.07.1.1015";"";""
"2015-08-30T13:35:32.671-05:00";"vincent";"2";"1.07.1.1015";"";""
"2015-08-30T13:43:24.942-05:00";"vincent";"1";"1.07.1.1015";"";""
"2015-08-30T13:43:30.897-05:00";"vincent";"2";"1.07.1.1015";"";""
I'm guessing the service should run under SYSTEM and I checked whether this was the case in services.msc but I wonder why my username instead comes up in this log file the day I installed the new Windows Updates.
Again reinstallation fixed it.