Wiktionary
straight face
n. (context idiomatic English) A face that is expressionless, especially not laughing.
WordNet
straight face
n. a serious facial expression giving no evidence of interest or amusement
Usage examples of "straight face".
Then, with a straight face, he proposed the addition, making it a Class D felony for any member of the legislature to commit adultery in Little Rock while the legislature was in session.
Not that that's prevented Foreign Minister Mueller from lying to us about it with a straight face.