Yes, I think you should put this on your resume. I actually think you should include it regardless of where you are applying (even industry).
In term of framing it, I would include it either in Work Experience or Extracirricular activies. It should be setup like any job (i.e. company name plus your title). Then the work experience bullets should describe the main roles/responsibilities you have and what you did to set it up.
In terms of the interview, you absolutely have to flag that the company would be run by someone else if you take this job. MBB will not be happy if you continue a side-company while working there. You need to make it very clear that MBB is your priority and your startup is not.