Your brain gives the illusion that you can, because it can switch quite quickly. But this is just like the illusion that you can see the whole world around you - it's not actually so. The proof is straightforward, and needs a friend.

One person holds up two fingers, one on each hand, and holds them up about a foot apart in front of them. The other person looks rapidly back and forth between the two fingers, switching their gaze from finger to finger twice a second in a regular rhythm. It's not that hard to do this.

The person holding up the fingers watches the eyes of the other person, and once they've established a rhythm they ask them a visual memory question. They will be unable to answer it without breaking rhythm on their eye movements, which the friend can observe.

Corollary - you at some level only have one internal screen which can either view external images, or internal ones. Not both at the same time.