A rather cursory Order of battle for Big Black River Bridge can be found in Pemberton's report. (OR 24/1 p. 267) Pemberton states that Green's and Cockrell's Brigades of Bowne's Division were present on the left and right of the line with Vaughn's East Tennessee Brigade in the centre. This OB is fleshed out in Bearss' third volume of his The Vicksburg Campaign. (pp. 688-689) Bearss provides a regimental listing for the aforementioned brigades. The only other units he mentions are the 4th Mississippi Infantry and A, 1st Mississippi Artillery. Bearss does not provide a citation for this list but, his research is usually impeccable on such details.
Ryan