I have some personal experience here as my DH and I have worked for the same company. Very similarly, I already worked there when DH interviewed.
Definitely do not seek out anyone to talk about how you working with your SO wouldn't affect work, you're not couple-y, etc. Only if asked about it, volunteer some casual information about how you both separate personal and work life.
There was some concern from higher ups about having us both on staff. But I had a good reputation as being professional and drama-free and DH was an excellent fit so they gave it a shot. It has worked out great.
Our jobs don't intersect much. But if we find ourselves at a meeting together, we sit separately. We treat each other like co-workers. Definitely no kissy face, hugs, pet names, touching, etc.
In fact, unless they're told, most people have no idea we're married. It has led to some really funny conversations when people notice that he and I have photos of the same child in our offices.
Good luck - hope he gets the job!