28-0 includes the Duke men and the Duke women. I believe the tally is 16 men's games and 12 women's games.
As far as the women's games go, there were two Duke-UNC games, one of which was 1999 when UNC was 28-8 and the ACC Tournament runner-up (back in the period between 1998 and 2000 when Duke and NC State made Final Fours, UNC made the Elite Eight once, Clemson was still really good, etc.). Was a really good game; tied at the half, before Duke went on a run to win by 10 (if I recall the final margin correctly).
The men's games I have seen in person have had more top matchups (3 against Duke-UNC, including a game in the Dean Dome in the year UNC made the Final Four; one game against Florida which was a top-ten matchup). As for the women's games, I have seen two Duke-UNC women's games. The women's game in 1999 was memorable because both teams were very good. The Duke-UNC women's game in 2000 was notable because Duke won 101-58. I also was at the Duke-NC State women's game in January 2008, when Lindsey Harding's jersey was retired.
I have seen UConn play in person, just not against Duke. I saw them in the 2003 Regional (believe it was against Boston College in the Sweet 16 and Purdue in the Elite Eight; might have been Notre Dame in the Sweet 16, as I believe Notre Dame was the fourth team in that Regional).