The structure that controls the passage of substances into and out of both plant and animal cells is the cell membrane.

Here's why:

* Cell membrane: This thin, flexible layer surrounds all cells and acts as a barrier. It's selectively permeable, meaning it allows some substances to pass through while blocking others. This control is crucial for maintaining the cell's internal environment and carrying out essential functions.

While plant cells also have a cell wall outside the cell membrane, this wall provides structural support and protection but doesn't play a direct role in regulating what enters and leaves the cell.