The "partial roll" – where your thumb strums only two or three string – is an essential chord-melody technique. Remember this: roll to the melody note but no further. For example, take the first chord in this arrangement: pick the 4th and 3rd strings with your thumb and let your thumb come to rest on the 2nd string. That will bring out the sound of the 2rd string (which happens to be the melody note). This arrangement is full of partial rolls. The quickest way to spot them? They're the ones with an "x" above one or more strings.
Notice that some of the chords are barre chords higher up on the neck. Look carefully at the first chord diagram in the fourth measure. It says "5 fr" beside it which means "fifth fret."
Follow the chord diagrams carefully and you'll hear the melody emerging. Now it's your job to find the rest of the notes and pick them. For example, on the word "Parsley" in m. 3, strum the chord as shown in the diagram for the melody on the syllable "Par - ", then reach up to the third fret with your left-hand pinky finger and pick (yes, pick, not strum) the note on " - sley." It's by interweaving chords and notes in this way that you can create the effect of playing harmony and melody simultaneously.