It should be strongly noted that anyone interested in composition should study 18th century counterpoint, as the ability to write good counter melodies is very important.
The example below is written in the style of a fugue. The subject is an eight measure long melodic line that is then repeated a 4th higher in the saxophones. The answer is a P4 higher in the saxophones, but it's entrance is only four measures after the trombones have started. This technique of beginning the answer before the subject has finished is called stretto. The trumpets then enter a P4 higher than the saxophones. During Bach's era the third entrance would have been in the tonic - the same starting pitch as the subject. This style of writing is not common to big band arrangements, but this writer has heard it used on several occasions.
The type of counterpoint below is very common to big band writing. The counter melody, in the tenor saxophones, is most active when the melody has a sustained note and visa versa. It is common for a blues melody to be stated twice and during the second playing a counterline is added to create variety.