The highlighted context that best shows the meaning of "face was as serious as stone" is:
"He nodded and ordered our Humvee to stop. We looked again. The boy wore shorts and sandals, but no shirt. He was filthy and very thin. I opened the door, and Lieutenant Ramirez scanned the perimeter. Nothing moved. His face was as serious as stone."
In this context, the description of Lieutenant Ramirez's face being "as serious as stone" indicates that he had a stern and unyielding expression, suggesting a sense of gravity and focused attention to the situation at hand.