A piano part of a big band arrangement uses notation where chords are marked and stems extend to both sides of noteheads:
My guess is that this is marking the highest note of the chord to play, as opposed to (more conventional) notation that only gives the chords and the rhythm.
Could you confirm if my assumption is right? Is this commonly used notation?
This is used occasionally and means exactly what you think it does: play those chords in that rhythm with those top notes. The exact voicing is up to the player.
Here's another example that's more explicit about the voicings:
Not uncommon in guitar or keyboard parts, or maybe in a 'short score' where all the instrument parts are condensed onto one or more staves. Yes, it means to play block chords under the given melody.
