"Obličej" is strictly "face", but "tvář" can mean either "face" or "cheek". So in this case you can use both, even though "obličej" is maybe more natural.
You define the meaning of "tvář" based on context, e.g. if you say: "Mám dvě tváře." it just means "I have two cheeks."
Then there is another word "líc/líce" (both variants of spelling are correct) and its meaning is simply "cheek". You cannot use it as "face".
As a side note. There seems to be one instance where one means an entire face yet would never use obličej but always tvář. Face to face. Tête-à-tête. This would always be "tváří v tvář".