This description is not detailed. The idea, like other post battle reports written during this period, was to provide a synopsis of the battle and to officially recognize the contributions of important subordinates.
To find a detailed description of how the main line was deployed, it is necessary to sift through the accounts of participants, written after the war.
Captain Samuel Hammond of South Carolina wrote that, "The second line will be composed of the continental regiment of Maryland troops, commanded by Lieutenant-Colonel Howard; on the left of the second line, falling back one hundred yards in its rear, a continuation of the second line, or third line, will be formed, advancing its left wing towards the enemy, so as to bring it nearly parallel with the left of the continental troops, upon the second line. The Virginia militia, commanded by Major Triplet, with the South-Carolina militia, commanded by Captain Beaty, will form to the right of the second line; the left nearly opposite to the right of the second line, one hundred yards in its rear; the right extending towards the enemy, so as to be opposite to or parallel with the second line."
The units numbered 3, 4, and 5 in the map below show what this formation would have looked like.
1 = Continental Light Dragoons, 2 = Mounted Militia, 3 = Right Wing of the Main Line, 4 = Continental Infantry, 5 = Left Wing of the Main Line, 6 = Right Wing of the Militia Line, 7 = Left Wing of the Militia Line, 8 = Skirmishers
What Hammond described seems unconventional. However, there is confirming evidence that it is correct. Major-General François-Jean de Chastellux (a member of the French expeditionary force in America) interviewed one of the Augusta county riflemen that served in this formation and learned that Morgan "divided his riflemen upon the two wings, so as to form, with the line, a kind of tenaille, which collected the whole fire, both directly and obliquely, on the center of the English…" He also wrote that he later met Morgan and that Morgan confirmed his understanding of how the battle was fought. (For examples of a what a tenaille can look like, see here and here).
This "tenaille"-like formation seems sensible for the occasion. By placing rifle-bearing militiamen 100 yards behind and to the side of the regulars, Morgan enabled these militia to aid the regulars with their fire, while at the same time shielding them from a British bayonet charge. Because the rifles of the militia had a much longer range than the muskets of the Continentals, both groups would have been able to commence firing on the British at the same time.
This formation also seems superior to the one usually attributed to the American main line in which the Continentals and militia are placed side-by-side. The two types of units had very different fighting styles. The Continentals fought in a tight formation, using tactics very similar to those of the British. At Cowpens, according to Thomas Young, "The regulars, under the command of Col. Howard, a very brave man, were formed in two ranks." The militia were less well disciplined, their rifles were slower-loading, they fought in a single rank (see statement by William Neel), and they were ill-equipped to withstand a bayonet charge. A bayonet charge directed against the militia on the main line would most likely have forced them to suddenly flee, leaving the Continentals dangerously exposed.
John Moncure's The Cowpens Staff Ride and Battlefield Tour webpage has a transcription of the statements by Daniel Morgan, Samuel Hammond, Thomas Young and William Neel.
Joseph Johnson's 1851 Traditions and Reminiscences Chiefly of the American Revolution in the South is the original source of Hammond's statement.
François-Jean de Chastellux's 1787 Travels in North-America, in the Years 1780, 1781, and 1782.