I know that perfect information games are the games that every player knows its situation and decisions in the game. But is it possible for a game which includes chance nodes to be a perfect information game?
The answer is yes. Perfect information concerns the case where "every player who is to take an action knows the current state of the game, meaning that he knows all the actions in the game that led to the current point in the play" (Maschler, Solan and Zamir, Game Theory, 2013, p. 44). If the action realised at a chance node is observed by all players making subsequent choices, the game has perfect information.
Some scholars like to speak about *games with perfect information and chance moves" to underline that the existence of chance moves is independent of the information ascribed to the players.